; $111241; OVERDUE FINES: 25¢ per day per item RETURNUKS LIBRARY MATERIALS: H Place in book return to remove charge from circulation records AN EMPIRICAL INVESTIGATION OF THE USEFULNESS OF EARNINGS IN PREDICTING FUTURE ENTERPRISE CASH FLOWS Bu John Edward Brooks A DISSERTATION Submitted to Michigan State University in partial rulfillment of the requirements for the degree of. DOCTOR OF PHILOSOPHY Department of Accounting 1981 ABSTRACT AN EMPIRICAL INVESTIGATION OF THE USEFULNESS OF EARNINGS IN PREDICTING FUTURE ENTERPRISE CASH FLOWS 89 John Edward Brooks The Financial Accounting Standards Board in its Statement of Financial Accounting Concepts No. 1 implies that there is a relationship between earnings and enterprise cash flows which is useful for predicting future enterprise cash flows. This dissertation examines the hypothesized relationship by using the Box-Jenkins time series analysis techniques. Financial data for thirty firms were taken from the quarterly COHPUSTAT tapes for the period beginning with the third quarter of 1964 and ending with the fourth quarter of 1978. A surrogate for enterprise cash flow was computed from the data in the quarterly statement of earnings and the annual statement of financial position. The cash flow series and the earnings series for each firm were used to form an ARIHA model and a transfer function/noise model (TF model) of the cash flow series for each firm. These models were used to make forecasts of the last ten observations of the cash flow series. The null hypothesis of no difference in forecasting performance was tested for each lead time. None of the. null hypotheses could be reJected at the .05 level. Depreciation was shown to be an important variable in the gTF model for cash flow. Therefore. firms were examined with respect to this variable. The percentage of depreciation to operating income before depreciation was used to partition the firms. Thirteen firms had . percentages of 35% or greater. The relative forecasting accuracy of the models for these firms was tested. Using the percentage squared error metric. the test for a forecast lead time of one was significant at the .04 level. Therefore. depreciation may be an important variable in establishing a useful transfer function relationship between earnings and cash flows. An examination of the TF models gave no insight into how the amount of depreciation affected the modelsr ACKNOWLEDGMENTS I would 'like to thank Dr. Ronald Marshall for serving as chairman of the disseration committee. His guidance was instrumental in my completion of the doctoral program at Michigan State University. Dr. Kenneth Janson provided a great amount of assistance regarding the methodology. His prompt and thorough reviews helped the writing of the dissertation to progress smoothly. Dr. Richard Simonds provided technical advice regarding the methodology. Computing services at Michigan State University and University of Florida were used during the preparation of the dissertation. The Script software package produced by the University of Waterloo was used to prepare the actual text. I would, like to thank Ernst and Whinney for providing funding for the dissertation. 1 Perhaps the most important people involved in the writing of this dissertation are my wife Julie and daughter Erica. They endured my ahsence during weekends and evenings without complaint and suffered my bad temperment when things were 'not going well. ii CONTENTS mun . me I I INTRODUCTION I I I I I I I I I I I I I I I I I I I p.- RESEARCH QUESTION . . . . . METHODOLOGY . . . . . . . . LIMITATIONS . . SUMMARY OF CHAPTER CONTENTS eeee 0000 III LITERAT‘RE REVIE“ a a I e o a e e a o e e a e‘ a a a 11 ANNUAL EARNINGS STUDIES . . 1 . . . . . . . . . ll QUARTERLY EARNINGS STUDIES . . . . . . . . . . . 15 CASH FLOW STUDIES . . . . . . . . . . . . . . . 17 SUMMARY . . . . . . . . . . . . . . . . . . . . 20 I I I I METHODOLOGY I I I I I I I I I I I I I I I I I I I I 22 ARIMA MODELS . . . . . . . . . . . . . . . . . . 22 Identification . . . . . . . . . . . . . . . 26 Estimation . . . . . . . . . . . . . . . . 28 Diagnostic Checking . . . . . . . . . . . 29 TRANSFER FUNCTION/NOISE MODELS . . . . . . . . . Si Prewhitening . . . . . . . . . . . . . . . . 33 Transfer Function Identification and Estimation . . . . . . . . . . . 36 Identification and Estimation of the Noise "OdIl I I I I I I I I I I I I I I I‘ I 38 Diagnostics for the TF Model . . . . . . . 88 SUPERIORITY OF TRANSFER FUNCTION/NOISE MODELS . 39 . 43 CHAPTER SUMMARY . . . . . . . . . . . . . . . IV. THE RELATIONSHIP BETWEEN CASH FLOW AND EARNINGS . . 44 NOTATION I I I I I I I I I I I I I I I I I I I I 44 CASE I I I I I I I I I I I I I I I I I I I I I I 46 CASE 2 I I I I I I I I I I I I I I I I I I I 5 1 CHAPTER sunnARY. I I I I I I I I I I I I I I I I I 53 V. VARIABLE DEFINITIONS AND DATA GATHERING . . . . . . 54 DEFINITION OF VARIABLES . . . . . . . . . . . 54 Justification for “From Operations” Variables.54 Earnings Variable . . . . . . . . . . . . . . 57 Cash Flow Variable . ... . . . . . . . . . . 58 iii CASH FLOW SURROGATE 6O DATA SELECTION . . . . . . . . . s . . . . . . . 64 Data Elements . . . . . . . . . . . . . . . . 65 Data Gathering . . . . . . . . . . . . . . . 65 CHAPTER SUMMARY . . . . . . . . . . . . . . . . 68 VI. MODELING AND FORECASTING . . . . . . . . . . . . . 7O MODELING e e a a a e a e a e e e a e e e e e e e 70 Univariate Models . . . . . . . . . . . . . . 71 Multivariate Models . . . . . . . . . . . . . 76 FORECASTING . . . . . . . . . . . . . . . . . . 78 ANALYSIS . . . . . . . . . . . . . . . . . . . . 79 Error Metrics . . . . . . . . . . . . . . . . 79 Statistical Hypotheses . . . . . . . . . . . 82 Results . . . . . . . . . . . . . . . . . . . 84 Controlling for Depreciation . . . . . . . . 98 Analysis of the Results . . . . . . . . . . 109 VII. SUMMARY. CONCLUSIONS. AND RECOMMENDATIONS . . . . 114 SUMMMY I I I I I I I I I I I I I I I I I I I 1 14 CONCLUSI DNS I I I I I I I I I I I I I I I I I 11 8 LIMITATIONS I I I I I I I I I I I I I I I I I 121 RECOMMENDATIONS . . . . . . . . . . . . . . . 122 6222211; 221: A. UNIVARIATE MODELS - CASH FLOWS . . . . . . . . . 124 B. UNIVARIATE MODELS - EARNINGS . . . . ... . . . . 126 C. TRANSFER FUNCTION MODELS . . . . . . . . . . . . 128 D. DEPRECIATION PERCENTAGES . . . . . . . . . . . . 130 E. TAIL AREAS OF THE CHI-SQUARE DISTRIBUTION . . . . 132 F. DIAGNOSTIC STATISTICS - UNIVARIATE CASH FLOW MODELS . . . . . . . . . . . . . . . . . . 133 G. DIAGNOSTIC STATISTICS - UNIVARIATE EARNINGS MODELS.135 H. DIAGNOSTIC STATISTICS - TRANSFER FUNCTION MODELS 137 BIBLIOGRAPHY I I I I I I I I I I I I I I I I I I I I I 139 iv Iabgg 4. 5. 6. 8. 9. 10. 11. 12. 13. 14. DATA ELEMENTS SAMPLE FIRMS . . . ERROR METRICS TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST RESULTS RESULTS RESULTS RESULTS RESULTS RESULTS RESULTS RESULTS RESULTS RESULTS RESULTS APE - PSE - CPVAE APE - PSE - CPVAE APE - PSE - CPVAE APE - PSE - LlST OF TABLES ALL FIRMS - ORIGIN 50 . ALL FIRMS - ORIGIN 50 . - ALL FIRMS - ORIGIN 50 ALL FIRMS - ALL ORIGINS ALL‘FIRMS - ALL ORIGINS - ALL FIRMS - ALL ORIGINS HIGH DEPRECIATION - ORIGIN 50 HIGH DEPRECIATION - ORIGIN 50 . -.HIGH DEPRECIATION - ORIGIN 50 HIGH DEPRECIATION - ALL ORIGINS HIGH DEPRECIATION - ALL ORIGINS 100 102 104 105 107 Chapter I INTRODUCTION The Securities and Exchange Commission requires companies to record transactions to permit the preparation 0? Pinancial statements in accordance with generally accepted accounting principles. Generally accepted accounting principles require that the Oirm’s accounting system be based on the accrual accounting model. The maJor alternative to the accrual model is the cash 910w model. This model is used by some small Firms not aQFected by the reporting requirements 0? the Securities and Exchange Commission and by most Oirms For tax reporting purposes. The accrual accounting model is more complex than the ‘cash Flow model. Accruals. deferrals. and allocations which are not perPormed in the cash Plow model are required by the accrual model. The process of calcUlating the accruals. deterrals. and allocations is not without cost. Because the accrual model is more costly to use. its use must be Justifiied based on the assumption that it provides more valuable information to the users of Financial statements than could be obtained From a cash oriented system. Generally accepted accounting principles are established by the Financial Accounting Standards Board. However. the 2 Securities and Exchange Commission can override the Financial Accounting Standards Board as they did by requiring reserve recognition accounting in the oil industry. The Financial Accounting Standards Board in its Statement of Financial Accounting Concepts No. 1 entitled Wei PM“ I‘m 1113121119.”. we T's states that: The primary focus of financial reporting is information about an enterprise’s performance provided by measures of earnings and its -components. Investors. creditors. and others who are concerned with assessing the prospects“ for enterprise net cash inflows are especially interested in that information. Their interest in an enterprise’s favorable cash flows leads primarily to an interest in information about its earnings rather than information directly about its cash flows. Financial statements that show only cash receipts and payments during a short period of time such as a year can not adequately indicate whether or not an enterprise’s performance is successful. Information about enterprise earnings provides a better indication of enterprise performance than information about current cash receipts and payments.(para. 43-44) The preceding statement implies that future enterprise cash flows are important to investors. creditors. and certain other users of financial statements. Also. it implies that there is a relationship between accrual earnings and future enterprise cash flows. Further. it implies that the relationship is more useful for predicting enterprise cash flows than any relationship between‘ past cash flows and future cash flows. Beaver and Demsti (1979.p.43) state that: The crux of the argument on behalf of accrual accounting rests on the premise that (1) reported 3 income under accrual accounting rules conveys more information than a less . ambitious cash-flow-oriented accounting system would. (2) accrual accounting is the most efficient means to convey this additional information. and as a corollary. (3) the ’value’ of such an additional information system exceeds its ’cost.’ They go on to conclude (p.45) that. “in our view. one challenge to accounting theorists is to address the primitive question of the propriety of the accrual concept of income." The research reported in this dissertation addresses the preceding challenge. 1.1 WW Based on the stated objective of financial reporting put forth by the Financial Accounting Standards Board. a test of the propriety of an accouhting model can be based on the ability of the model to predict fUture enterprise cash flows. Although the Financial Accounting Standards Board suggests that the accrual accounting model is useful for predicting enterprise caSh flows .no empirical evidence is available to support this hypothesized relationship. Further. the Financial Accounting Standards Board suggests that “measures of earnings“ are the primary focus of financial reporting. Thus a test of an accounting model should center on its ability to predict future enterprise cash flows based on the earnings number generated by the model. 4 Given the cash basis of accounting as a base level of information. the research question addressed by the reported research is : does the addition of the earnings number from the accrual accounting model to the information set provided by the past enterprise cash flows permit better predictions of future enterprise cash flows than predictions made only from past enterprise cash flows? The research does not attempt to address the cost-benefit issue raised by Beaver and Demski. nor does the research address the form of communication issue. The research question is significant for several reasons. First. although the research will not permit a conclusive statement about the propriety of the accrual accounting model. it may permit conclusions about the appropriateness of the accrual model given the stated obJectives of the Financial Accounting Standards Board. The use of the accrual accounting model may be Justified based on other obJectives for financial reporting. Therefore. the research addresses the issue of the appropriateness of the accrual accounting model given the financial reporting obJectives rather than appropriateness of the model given other obJectives. Second. in order to address the cost-benefit question raised by Beaver and Demski it is necessary to know what benefit is achieved with regard to the obJectives of financial reporting by- using the accrual accounting model in conJunction with the cash flow model. The reported research 5 addresses this issue. Third. although the limited scope of the research may not allow for .conclusions regarding the appropriateness of the accrual accounting model. it provides information which may be useful to researchers wishing to investigate the} relationship between the obJectives of financial reporting and accounting models. 1-2 W The research reported in this dissertation uses time series analysis as the primary methodology. Specifically. forecasting models were constructed using the Box-Jenkins modeling techniques. Financial data were taken from the quarterly COMPUSTAT tapes for the period beginning with the third quarter of 1964 and ending with the fourth quarter of 1978. This provided sixty observations for each firm used in the study. Cash flow numbers were constructed from the quarterly financial data. ‘The quarterly earningf and net cash flow series were then used in the modeling process. A univariate model was constructed on the first fifty observations in each time series. The net cash flow based model was used to forecast future cash flows. The univariate model based on accrual earnings was used in the model building process for the multivariate model. The multivariate model was then used to forecast cash flows. The modeling and forecasting were accomplished with the aid of computer programs entitled A Computer Erggram for EL; 6 Analgsiz gfi Time Series Models Using the Box-dentin; Philosophy by Pack and SHORTE: A Box-Jenking' lime Series Analysig ngtjng Eeatgring Concise Output; by Janson. Using the two models for each firm a set of forecasts were made for the last ten observations of the net cash flow series for each firm. The forecasting process consisted of generating forecasts for one through ten steps ahead from an origin at the end of quarter fifty. The origin was moved one quarter Iahead. the parameters off the models were reestimated.' and forecasts were made for each step ahead subJect to the sixty observation limit. Three measures of forecast error were computed for one through ten step ahead forecasts. The measures of forecast error were then analyzed utilizing the P35 program of the Biomediga; Compute: Program; 2-Series produced by the University of California. 1.3 LLfllTA ION The study reported in this dissertation investigated the relationship between accrual earnings and enterprise net cash flows.' Several factors related to the methodology and the data impose limitations on the interpretation of the results. These limitations are discussed below. Cash flow information was not reported for all periods covered by the study. Therefore. net enterprise cash flows had to be constructed from available financial accounting 7 data. In order to obtain a: sufficient number of observations for the modeling and forecasting process. it was necessary to use quarterly data. Complete earnings statement information was not required in publicly available documents until 1970. However. some firms reported detailed earnings information on a voluntary basis prior to 1970. The statement of financial position was not required in publicly available documents until 1975. Little voluntary reporting of this information is evident. Therefore. a surrogate for enterprise cash flow had to be constructed from available earnings statement information. The computation of the surrogate. due to data restrictions. does not include the effect of the change in accruals. deferrals. and inventories during the accounting period. These items are minor when compared to depreciation. which is the maJor difference between cash flow and earnings for industrial companies. The surrogate represents the best estimate of cash flow that an investor could have made given the information available. The interpretation of the empirical results of the study must be tempered by the possibility of a significant difference ‘lhbetween the surrogate and the actual cash flow number. Another limitation was imposed by the data. It was not possible to use a random sample in the study due to the small number of firms which consistently reported quarterly data with enough ‘ detail to permit the computation of a S meaningful surrogate. This means that the results of the research can not be generalized to all firms without further investigation into the characteristics of reporting versus nonreporting firms. The reported research is a Joint test of the predictive relationship between earnings and cash flow. and the ability of the methodology to detect any existing relationship. The time series analysis technique used in the research assumes that the underlying process is a stationary process. which has homogeneity of variance. Since many forces act on the firm and the economy which may change the underlying process generating cash flows and earnings. there is a risk in using data spanning long periods. The modeling and forecasting procedures used in the research utilized data spanning sixty quarters which introduces the possibility of the form of the process changing. If the process does change. the forecasting model identified from the data may ‘be inadequate. ‘ The methodology also requires the use of a large number of observations from the series. With respect to the univariate models. the fifty observations used for modeling should provide acceptable statistical precision based on research by Loreh and McKeown(197S). Using quarterly earnings data. they found that as few as thirty observations may be used without severe deterioration of .the ability to determine the form of the model and estimate its parameters. 9 Box and Jenkins (1970. pp. 374) suggest that fifty observations are sufficient for the identification and estimation of multivariate models. Differencing of the data in order to obtain stationarity will bring the number of useful observations slightly below the recommended level. No study similar to the one performed by Lorek and McKeown on univariate models has been performed on multivariate models. Therefore. it is not clear if the small deviation from the fifty observation rule of thumb is significant. 1-4 §!flfl631.QE.QEAEIEB.£QNIENI§ The dissertation is divided into five chapters. Chapter I is the introduction to the reported research. A brief discussion of the problem. the research question. and the methodology is presented. The limitations of the study are also presented. Chapter II presents the literature review. The review is divided into three areas. studies on the time series properties of annual accounting numbers. studies on the time series properties of quarterly accounting numbers. and studies on cash flow numbers. The third chapter presents a discussion of the methodology used in the research. This presentation is made to permit a reader unfamiliar with the methodology to understand the presented research. 10 Chapter IV presents a discussion of the possible reasons for expecting a predictive relationship between earnings and net cash flow. This issue is discussed as it relates to the methodology used in the research. Chapter V presents the results of the data gathering and modeling. The computation of the cash flow surrogate is discussed in detail. The models for each firm are presented. The sixth chapter presents the empirical results of the study. The results of the forecasting and the statistical analysis are presented. Chapter VII presents a summary of the research. The conclusions and recommendations are developed and presented. Chapter II LITERATURE REVIEW Many researchers have shown interest in forecasting or in the time series properties of various income measures. The research can be divided into studies examining the properties of annual accounting numbers and those examining quarterly accounting numbers. This chapter provides a review of the maJor studies related to the research reported in this dissertation. A review of annual earnings studies is presented first. Next. a review of quarterly ‘earnings studies is presented. The last section of the chapter provides a discussion of studies involving enterprise cash flows. 2-1 LILALNN mamas: Frank'(196S) studied the ability of past values of current cost income and historical cost income to predict future values of their respective income measures using linear extrapolations of the past series. He also investigated the ability of current cost income to forecast historical cost income. His measures of income excluded nonrecurring items. The study found that current cost income did not provide superior forecasts of either measure. 11 12 ‘ Simmons and Gray (1969) investigated the ability of three income measures to predict values of their respective series. This study used simulations to generate the data. They found that the predictive ability varied with the growth pattern assumed in the simulation models. Revsine (1971) criticized the preceding studies on the basis that income measures are artifacts. He states that "unless there is some compelling evidence to suggest that knowledge of future artifact values is useful. the reason for desiring to predict future income levels is unclear.“ Revsine suggests that forecasts of income measures can be Justified by either: ”(1) an assumed correspondence between some particular income measure and certain real events of interest to users. or (2) an appeal to the 'efficient market hypothesis.’“ The second Justification is based on the assumption that the income measure influences the price of 'securities. He argues that this Justification is transitory and therefore the first Justification provides the strongest argument for the prediction of an income measure. Beaver (1970) suggests that: The time series behavior of earnings is an important area for empirical research because of its implications for research in several areas of accounting and finance. Although many other .examples could be provided. three ’accounting’ issues immediately come to mind: (1) income ‘smoothing. (2) the relative forecast ability of alternative income measures. and (3) interim reporting. - .- 13 Beaver goes on to say that serious doubts can be raised with the propriety of forecasting measured income rather than “true“ income. Several studies using the Box-Jenkins methodology have been performed using annual accounting numbers. Watts and Leftwich (1977) investigated the time properties of annual earnings available for common. They were interested in whether or not a random walk model provided better one step ahead forecasts than firm specific models. The study showed that the random walk model was able to “outpredict” the firm specific models. The results of this study are questionable. They reported that there was some evidence that the underlying series was not stationary and that they could not use a logarithmic transformation to obtain stationarity because some of the data points were negative. This problem could have been eliminated by Ichanging the level of the series. _ i I I Albrecht. Lookabill. and McKeown (1977) studied the same issue. They introduced an additional variable by deflating the earnings available for common using the stockholders’ equity of the previous period. Using a different set of data they concluded that a random walk“ with a drift and a simple random walk provide predictions of .the nondeflated and deflated series. respectively. which are as good as those provided by the firm specific models. 14 Manegold (1978) investigated the use of multivariate models for forecasting accounting data. ‘ His forecasted variable (EBT) was earnings before taxes. excluding extraordinary items. nonoperating income. and nonoperating expenses. He presented a set of theoretical arguments for the superiority of multivariate models over univariate models in forecasting. These arguments by Pierce and Nelson are presented in Chapter III. Manegold constructed a component based model and a univariate model for each of the 27 firms in the sample. The component based models were constructed by first decomposing EBT into operating income before depreciation. depreciation. and interest charges. Each component was then modeled using its components. For instanae. operating income before depreciation was modeled as the product of units sold and operating margin. The number of units sold was modeled as a transfer function with an industry index as the additional variable. Operating margin was modeled as a univariate model.’ The forecasts of all the components were then combined to provide a forecast of EBT. He was unable to demonstrate the superiority of the multivariate model over the univariate model for forecasting EBT. 15 2.2' QUARIERLI W SMILES Brown and Niederhoffer (1968) examined' the predictive content of quarterly earnings per share. They forecasted annual earnings per share using quarterly earnings per share in various hypothesized models. This study formed the basis for a recent study by Lorek which used the Box-Jenkins methodology. Several other studies using the same methodology have been conducted on quarterly accounting data. These studies are described in this section. Lorek. McDonald. and Pat: (1976) compared management forecasts of quarterly earnings with those generated by firm specific univariate Box-Jenkins models. The forecasts from the models outperformed the management forecasts. They reported that 'most of their models contained seasonal parameters or seasonal differencing. Further studies have confirmed this finding. Foster (1977) examined the time series properties of quarterly earnings. sales. and expenses. Firm specific Box-Jenkins models were constructed for sixty-nine firms. One step ahead forecasts from the models were compared to forecasts from five hypothesized general models. A general model which incorporated an autoregressive seasonal factor performed .better than the firm specific models. This suggests that the firm specific models may have been overfitted. 16 Griffin (1977) examined ‘the time series behavior of quarterly earnings available for common. General models were formulated based on the mean values for the autocorrelation function and partial autocorrelation function for a cross section of ninety-four firms. Estimates of the parameters were then computed for each firm. The general models were then evaluated based on the autocorrelation and partial autocorrelation functions of the residuals. This research suggests that the quarterly earnings process may be characterized as either “a multiplicative first-order autoregressive process. or a multiplicative first order moving average process in first differences of the four-period difference of quarterly earnings." He suggests that Foster’s model does not fully account for the seasonality. Brown and Rozeff (1979) compared the forecasting ability of a general model which they developed to the forecasting ability of the general models of Foster and Griffin and to the forecasting ability of firm specific models. Earnings per share was the variable of interest. This study evaluated the models for one. five. and nine step ahead forecasts. Four sets of forecasts were produced with the parameters of the models being reestimated using all the data up to the beginning of the forecast period. They concluded that the relative forecasting accuracy of the various models changed over increasing forecast horizons. 17 Specifically. they found that a model containing a first order autoregressive parameter. a seasonal moving average parameter. and a seasonal difference of four periods outperformed or performed as well as the other models over all forecast horizons. A study by Lorek (1979) examined various models’ ability to forecast net annual earnings. He examined the ability of the general models suggested by Brown and Rozeff. Griffin. and Foster. firm specific models; and five simplistic models to forecast the variable of interest. He reported results which cast doubt on the superiority of the Brown and Rozeff model. 2-3 QAEEELMEMIES‘. Staubus (1965) investigated the association of financial accounting variables with common stock values. The variables investigated were: (1) earnings available for common. (2) current flow. which was computed by adding depreciation. depletion. and amortization to earnings. (3) net recurring funds flow. which was computed by excluding the effect of securities transactions. the sale or purchase of plant assets. tax adJustments. and other nonrecurring events. (4) cash dividends declared. and (5) the book value of common equity. The common stock values used in the study were computed values based on the discounted value of a known succeeding market value and the dividends paid during the 18 holding period. The correlation between the common stock values and the variables was examined over several discount periods. In order to clarify the design of the Staubus study. consider the following situation. An investor makes a decision. based on the values of the five variables. to buy and hold common stock. The investor was given the sum of the past 1. 2. 3. g; 4 values of the variables as information on which to base a decision. Some years after the decision. the investor wishes to know how well the variable he used in the decision making process correlates with the present value (at the decision date) of the return from the investment (which is now known). The results of the Staubus ‘study indicate that current flow exhibited the largest correlation for one year and two year variables while net recurring funds flow was the best for the three year and four year flow variables. Earnings was inferior to current flow over all periods and inferior to net ’recurring funds gflow for the three and four year variables. The surrogate for cash flow used in this dissertation is similar to the net recurring funds flow .variable. The fact that the funds flow variable provided superior correlations with the common stock values may indicate the surrogate is important to investors. Ball and Brown (1968) formed expectation models using net income. net income before nonrecurring items. and cash flow 19 as approximated by operating earnings. The models were used to separate the firms into good news and bad news categories with respect to the variables of interest. Abnormal performance indexes were then computed for the year preceding the announcement of the variable. They reported that net income provided the largest API. 1.071 for positive errors and 0.907 for negative forecast errors. Operating income. the cash flow surrogate. had API values of 1.070 for the positive errors and 0.917 for the negative errors. Net income before nonrecurring items produced API values of 1.068 for positive errors and 0.911 for negative errors. It is not clear whether or not the values are different across variables in a statistical sense. The evidence seems to support the findings of the study by Staubus that some surrogates for cash flow may be highly associated with security values. Cheung (1977) attempted to predict a net cash transfer variable using accounting data. The net cash transfer variable was computed by summing paid diVidends. interest paid. the net disbursement from the repurchase or sale of all classes of stock. and the net cash disbursement from financing activities. He found that given a knowledge of past cash flows. the use of accounting data as an additional independent variable provided no additional information. However. out of the variables -tested. earnings numbers appear to be more useful in predicting cash flows than are theichomponents. 20 Cheung’s study has a direct relationship to the research reported in this dissertation. Box-Jenkins methodology was used to formulate the prediction models. The cash flow variable used in the Cheung study is equivalent to cash income less net purchase of assets. The cash variable used in this dissertation is a surrogate for cash income from recurring operations. For an all equity firm. cash income less net purchase of assets is identical to dividends plus net disbursements from stock transactions. Thus. the dividend series was used as the maJor variable in the Cheung study given that no stock was repurchased. Dividends are only one element of enterprise cash flow and only one factor affecting investor wealth. The Cheung study does not provide a fair test of the accrual accounting model within the framework of the Financial Accounting Standards Board’s -obJectives because the variable to be predicted was cash .flow to the investor not enterprise cash flow. 2-4 W This chapter reported several studies which relate to the work done in this dissertation. Some observations can be made from the reported literature. First. it appears that no consistent empirical evidence exists for a general model of quarterly earnings. Second. .any .theoretical advantage of the multivariate models over the univariate models for forecasting accounting variables may be difficult to 21 demonstrate empirically. Finally. the cash flow surrogate used in this study appears to be associated with common stock prices. Therefore. forecasting the surrogate may be of interest in itself. Chapter III METHODOLOGY The research reported in this dissertation uses the Box-Jenkins modeling techniques to build forecasting models for quarterly cash flows. The methodology has been used in several studies to form prediction models for annual or quarterly net income (Lorek. 1979: Foster. 1977) ‘Brown and Rozeff. 1979). Two types of models are used in the study. the autoregressive integrated moving average model and the transfer function/noise model. This chapter describes the model building process for each of these types of models. The autoregressive integrated moving average (ARIMA) model is discussed first. A discussion of the transfer function/noise model follows. The last section of the chapter presents a discussion of the conditions required for the transfer function/noise model to provide forecasts which are superior to those provided by the ARIMA model. 3-1 mums ARIMA models can be used to forecast values of a variable from the past time series of .the variable. This class of model was introduced in the accounting literature by Mabert and Radcliffe in 1974. These models describe the dynamics of 22 23 the process generating the variable using a set of autoregressive. moving average. and differencing terms. An underlying assumption of the modeling technique is that the time series is stationary. If the underlying series is not stationary. various transformations can be performed on the data in order to obtain a stationary series. Differencing is one of the most typical transformations used to obtain stationarity. Box and Jenkins (1976) provide a set of symbols for operators .which have become a standard for providing a concise mathematical description of ARIMA models. Denoting cash flow as CF. the general form of the model is 11(3) pies) (1-BS)D (1-B)d CFt .. so + 8(B) 9135) at I. where B I backshift operator such that B(CFt) 8 CF’t_1 . m3) . 1 - p19 - fizaz - "‘-'¢pnP . with. 11's representing autoregressive parameters. I 0698) - 1 - al’es - “21325 - - pPBPS . with Bgfs representing seasonal autoregressive parameters. s - the seasonal span. D I the order of the seasonal differencing. d = the order of the consecutive differencing. 24 85 I a constant which represents a deterministic trend. 9(3) . I-Sla -8282 - -eqnq . with Gangrepresenting moving average parameters. e’ms) 1 - e’les - 93325 - - 93625 . with 8:5 representing seasonal moving average parameters. and at 8 current disturbance term which is assumed to be independently distributed as normal variables having a zero mean and a constant variance . A short explanation of the parameters p. P. q. and 0 is in order. With respect to the p parameter. it can be seen from the model that it represents the number of past values of the independent variable (past cash flows) on which the dependent variable (current cash flow) can said to be ”regressed.“ Hence. the term autoregressive. In the case of a series which has been differenced in order to obtain stationarity. the regression is on the values of the differenced series. The P parameter can viewed in the same way with respect to past values of the series at seasonal intervals. The q parameter represents the number of past random shocks which affect the dependent variable. Likewise. the 0 parameter serves the same function for seasonal intervals of the past random shocks. 25 The conventional notation for the model is (p.d.q) X (P.D.G) . It is assumed that the differencing operations performed on the series will yield a stationary series. If this condition does not hold. then additional operations. such as taking the natural logarithm. must be performed until the stationarity condition is satisfied. An example of a simple model will serve to illustrate and clarify the above notation. Assume the following model. (1.1.1) X (0.0.0). Assuming that Oh I 0. the model can be written as (1 - HEB) (1 - B) CFt I (1 -‘OHB) at . Because P. D. and 0 are zero. the seasonal terms all go to one. The value of d is one. This produces the single difference term. The single autoregressive parameter is the result of p being equal to one. Likewise. the single moving average parameter is the result of q being equal to one. Expanding the model yields (1 ”513) cert -CFt_1)-at-81a . Rearranging. the model becomes CFt' CFt-‘I I ”ImFt-I " CFt-Z ) + '1: - eI'tz-I' ‘ The building of an ARIMA model follows a three stage process. These stages are identification. estimation. and_ diagnostic checking. The following sections describe these steps in the model building process. 26 3-1-1 New I The goal of the identification stage of the model building process is to select several possible models of the form presented above. That is. the order of p. d. q. P. D. G and the seasonal factor must be determined. This is accomplished primarily with the aid of the sample autocorrelation and partial autocorrelation functions. Several models are typically identified because the sample autocorrelations and partial autocorrelations are subJect to sampling error and therefore may be difficult to match with a theoretical function. More is presented on this issue in the following paragraphs. The first step in the identification process is to ;xamine the series in order to determine the transformations required to convert the original series into a stationary series. This is accomplished with a plot of the series and the sample autocorrelation function. The. plot can be inspected to determine if the level of the series is constant and if the variance of the series is constant. If the sample autocorrelations fail to die out rapidly. nonstationarity is suspected. This is because the observations of a nonstationary series' will tend to be on one or the other side of the sample mean for many periods. If nonstationarity appears to be a problem then a consecutive difference or a seasonal difference can‘ be taken. The plot of the transformed series and its sample 27 autocorrelation function can then be examined to determine if more differencing or other transformations are necessary. Once the order of differencing is determined. the process of identifying the appropriate orders of p.q.P. and 0 can begin. Each form of the ARIMA model has a theoretical autocorrelation function and partial autocorrelation function. The orders of p. q. P. and 0 are determined by manually matching the sample autocorrelation and partial autocorrelation functions to the theoretical functions for a particular form of the model. In inspecting the sample autocorrelation and partial autocorrelation functions. one looks for evidence of the characteristics which would be exhibited by the theoretical functions. Three general statements can be made about the theoretical autocorrelation and partial autocorrelation functions: 1. An autoregressive process of order p exhibits an autocorrelation function which tails off after lag p and a partial autocorrelation function which has a cutoff after lag p. 2. The autocorrelation function of a moving average process of order q has a cutoff after lag q while the partial autocorrelation function tails off after laq q. 3. Mixed processes exhibit autocorrelation and partial autocorrelation functions which tail off in a mixture of exponentials and damped sine waves after the first q-p legs and p-q lags respectively. 28 Because of . the sampling error in the sample autocorrelation and partial autocorrelation functions. it is unlikely. that the sample values will perfectly match a theoretical set of functions. Therefore. it is likely that several models will be selected as feasible models for the series. Values for the parameters in these models are estimated and various diagnostics are used in order to‘ select a final model. 3-1-2 mm During the estimation stage of the model building process. the values for the autoregressive and moving average parameters are determined. Preliminary estimates of the parameter values are obtained from the relationships that link the parameters and the autocorrelations. An iterative process is then used to obtain the maximum likelihood ‘estimates of the parameters. Box and Jenkins (1976. Chapter 6) provide a detailed discussion on obtaining the preliminary estimates of the parameter values. They include a set of tables which relate the sample autocorrelations to the parameter values for several common forms of the models. thereby avoiding the need for manual computation of the estimates. The iterative process of obtaining the maximum likelihood estimates of the parameters is presented in Box and Jankins (1976). This step in the modeling process is generally accomplished with the 29 aid of computer programs such as the ones used in this study. 3- 1-3 W 9.11.2..._.sckin After generating the parameter estimates for the identified models. the process of selecting the best model can begin. Several factors are used to operationalize the word "best.“ If the posited model adequately describes the underlying dynamics of the system. then the residuals should represent random noise. That is. they should exhibit no significant pattern in their autocorrelation function. Thus. this is one of the factors used in determining the appropriateness of a model. Other factors include parsimony and economic sinsibility. These ideas are discussed in the following paragraphs. Parsimony is the concept of adequately modeling the process with the least number of parameters. Therex is a duality between the 'autoregressive and moving average processes. A stationary autoregressive process with a finite number of parameters can be represented as a moving average process having an infinite number of parameters. Likewise. an invertible moving average process can be represented as an autoregressive process with an infinite number of terms. These facts coupled with the sampling variation of the autocorrelation function can lead to selecting models which are overly complex. 30 Usually something is known about the process which is being modeled. For instance. many quarterly time series can be expected to exhibit a relationship between observations four periods apart. Thus. the model for the series should not be expected to contain terms having a seasonal component at intervals such as five or six. The use of this concept in evaluating models is known as economic sensibility. With respect to evaluating the residuals. several procedures can be used. First. a plot of the residuals and their autocorrelation function is useful in checking for patterns in the residuals. From the plot of the residuals. one can inspect for the stationarity of the residuals and for constant variance. Inspection of the plot of the residuals is particularly important when Judging the "goodness" of the model by the residual mean square error. It is possible to generate models which exhibit small residual mean square error which are totally inadequate. These models exhibit. residuals which run consistently negative or positive in one portion of the series and then reverse in another portion of the series. If the residuals are random noise. then the autocorrelation function of the residuals should show no significant pattern. Two statistics have been developed to test if the autocorrelations of the residuals taken as a whole exhibit any_ pattern. The first of these is the Box-Pierce 0 statistic. This statistic is generated by most of the time 31 series software packages including the one used in this study. The statistic is compared to a chi-square distribution. LJung and Box (1978) reported that the statistic was biased downward. They proposed a statistic which eliminates the bias found in the Box-Pierce statistic. A solution to the problem of the biased statistic which is computed by most software packages is to use the LJung- Box statistic if the Box-Pierce statistic is close to the reJect region. The Box-Pierce statistic is reported in Appendices F and o for each of the ARIMA models. . The previous sections have presented the notation used to describe ARIMA models. An example of the use of the notation was given. The three stages of the modeling process were described in summary fashion. Rehders desiring a more complete discussion of the modeling process are encouraged to refer to either Box and Jenkins (1976) or Nelson (1973). 3-2 WWlfifl—LLES Transfer fUnction/noise models (TF) incorporate the structural relationships between the output variable and input variables into a forecasting model for the output variable. In this study only one input variable is used. earnings. Denoting earnings as E. the general form of the model is d(B) cft I w(B) .t-b + nt where 32 r d(B) 1 dlB dZBz drB. cft- an observation of the CF series suitably differenced to obtain stationarity. 2 s 111(3) - “’0 0113 ”28 ea. ”SB 1 et_ 3 is an observation from the earnings series. E. suitably differenced to obtain stationarity. b = the time lag in the response of cftto a change in "t.= is an observation from the stationary noise model which is an ARIMA process describing the noise remaining after the application of the transfer function. It is important to note that the forecasts made from a .transfer function depend on the past values of the output and input variables. This can be illustrated with a simple model. A shorthand way of describing a transfer function model is by giving the order of r.s. and b. For example. the simple model (1.1.1) can be written as (1 - dB) cft- (wo- U19)It_1 4- nt which can be rewritten as - - + ”t cat-I ' mo"1:--1 "I't-z -t Rearranging the terms produces 33 cft = dcft_1 + woet_l - Inlet:2 + "t . In forecasting. the unknown values of the cf series can be found by substitution. The construction of TF models follows several steps. The two maJor steps are the formulation of the transfer function and the noise model. Several procedures are required in order to perform these steps. They are described in the following sections. 3.2.1 Prgwhitgning In order to identify the form of the transfer function. the cross correlation function between the prewhitened input series and the correspondingly transformed output series is utilized. By examining another form of the transfer function model. it is possible to develop a relationship between the parameters of the model developed on the previous page and the cross correlation function. This relationship can then be used in the same manner as the autocorrelation and partial autocorrelation functions are used in determining the form of the ARIMA model. This section contains a development of the relationship between the d(B) and w(B) terms and the cross correlation function of the prewhitened input series and the correspondingly transformed output series. The TF model previously described can be written in another form as follows: 34 cft I v(B) et + nt where - v(B) - v0 + v18 + v2 92 + is the impulse response function. cft is an observation of the stationary cash flow series. et is an observation from the stationary earnings series. and nt is an” observation from the stationary noise series. The impulse response function is equivalent to w(B)Bb /d(B) where b represent; the time lag in the response of cft to a change in e. By equating coefficients of B in the relationship between the v(B). d(B). and w(B) terms. the following set of relationships is obtained: vJ I 0 for J ( b + + e e e + + vJ I 61.3;1 d2 vJ_2 dr vJ_r w0 for J 8 b V . d + d V + e e e + d V - F J 1 vJ-l 2 J-2 r J-r wJ-b or J'D+I: b+210eef 0+5 v I d v + d v + ... + d v J 1 J-l 2 J-2 :- J-r for J ) b + s. 35 In practice. the above relationships are used to determine the form of the transfer function from estimates of the impulse response function. The impulse response function can be determined by an examination of the cross correlation function of the prewhitened input series and the correspondingly transformed output series. It can be shown (Box and Jenkins. 1976 pp.380) that the cross correlation function between the prewhitened input and the correspondingly transformed output series is directly proportional to the impulse response function. The relationship is as follows: vJ I px,y,(J) cry,/ ax, where x’ and y’ are the transformed input and‘ output respectively. The J subscript on the impulse response weight corresponds to the lag term on the cross correlation between the transformed series. Prewhitening is simply the process of transforming the series by multiplying by the inverse of the ARIMA model which describes the input series. For example. in order to obtain the prewhitened series 1’. the following transformation is performed: a: I xt ( Ux(3)/ 9x(3) ). t Thus. one of the first steps in determining the transfer function is to model the input series. This is accomplished 36 with the procedures described earlier in this chapter. The effect of the prewhitening is to transform the input series into an uncorrelated white noise series. 3-2-2 WWWMW Inspection of the cross correlation function between the prewhitened input and the transformed output is used to identify the form of the transfer function. Because the cross correlation function is directly proportional to the impulse response function. estimates of the impulse response weights can be obtained. These estimates are then used to determine the order of r.s.and b in the transfer function. The identification process involves manually matching the sample impulse response function to‘theoretical functions generated by models with varying values of r. b. and s. In general. the impulse response weights follow the pattern described below: 1. There will be b zero values of the impulse response weights beginning with vb . 2. There will be a further (s - r + 1) values following no fixed pattern. If s < r. no such values occur. 3. Further values of vJ with J > (b + s - r + 1) follow the pattern dictated by a difference equation of order r which has r starting values. Starting values for J ( b will be zero. 37 For example. a model with r I 2. b I 3. and s I 2 should exhibit impulse response weights which are characterized by the following: 1. v . v . and v will all be zero. 0 1 2 2. v3 will not be zero and will not be part of a pattern. It represents the further (s - r + 1) values following no fixed pattern as explained in point two above. 3. v and v provide starting values for a double 4 5 exponential decay determined by the difference equation v - d 'I O for'J ) 5. J le-l 2 The identification of the form of the transfer function - d 2")— using the cross correlation function has the same difficulties as the identification process for the ARIMA models. Because of sampling error the cross correlations may not conform exactly to a theoretical pattern. 2 'After the form of the transfer function is identified. the parameters of the model can be estimated. Preliminary estimates can be derived from the relationship ’between the impulse response weights and .the d and w parameters previously described. These estimates are then used as the istarting point for an iterative process which generates the maximum likelihood estimate of the value for each parameter. This last step is performed by the time series software package. 38 3.2.3 wmmumugmm The residuals remaining after the application of the transfer function provide the basis for the identification of the noise model. By examining the autocorrelation function of these residuals it is possible to determine the form of this ARIMA process. This is accomplished using the techniques described in the sections of this chapter dealing with the ARIMA model. Again. the software is used to provide maximum likelihood estimates of the parameters. 3-2-4 W £91; .4.“ IE unis; Hithin the TF model. there are two sources for model inadequacy. The transfer function and/or the noise model may be misspecified. It is possible to examine various cross correlation and autocorrelation functions to determine if either of the components of the TF model are misspecified. ‘ The first step in examining the adequacy of the model is to examine the autocorrelation of the residuals from the fitted TF model. As with the ARIMA model. a’ correctly specified TF model should possess residuals which are uncorrelated white noise. Thus. evidence of any significant autocorrelation in the residuals suggests that the TF model is inadequate- ‘ The 0 statistic proposed by Box and Jenkins ( 1976. pp. 894) can be used to test for any significant pattern in the autocorrelation 'function of the residuals. This statistic is similar to the Box-Pierce statistic and 39 was computed for each model. The value of the statistic is reported in Appendix H for each of the models selected. .If the model is found to be inadequate. investigation is required to determine the cause of the inadequacy. By examining the cross correlation function of the prewhitened input and the residuals. it is possible to determine if the TF model inadequacy is caused by misspecification of the transfer function or the noise model. If the residuals are cross correlated with the prewhitened input series and the residuals exhibit significant autocorrelations. then the transfer function has been misspecified. This is true even if the noise model has been specified correctly. However. if the cross correlations are not significant but the residuals are ~autocorrelated. then the noise model has been misspecified. The 8 statistic. which is identical to the 0 statistic except that the cross correlations rather than the autocorrelations are used. can be used to itest for significant patterns in 'the cross correlations. This statistic was used in this study when model inadequacy was suggested by the 0 statistic. 3.3 WEWWW The research hypothesis investigated in athis paper deals with the prediction of cash flows. The univariate model which is based only on past cash flows is hypothesized to produce less accurate forecasts than the TF model which is 40 based on earnings and cash flows. Therefore. it is" important to understand the relative predictive accuracy of the two types of models. This issue is discussed in this section of the paper. All of the arguments presented are based on theoretical considerations and ignore the possibility of misspecification due to sampling error. Nelson (1975) has shown that the TF model should never perform worse in a forecasting context than the ARIMA model. lntuitively. this is because the TF model contains all the information resident in the output series *plus any information resident in the relationship between the input and output series. Nelson analytically examined a situation where 2(t). x(t) and y(t) are series which are described by a moving average process of order one. The relationship between the series is assumed to be 2(t) I x(t) + y(t). Independence is assumed between x(t) and y(t). He was able to show that the residual variance of the forecasts from the TF and the ARIHA model have the following relationship: «2-(u2-r «2)-d2(9 -e >2+a2(o --9 )2/1-92 z x y x x z y y z z where the Q‘and firparameters are from the ARIMA models. The left side of the equation represents the reduction in mean square forecast error of the TF model compared to the ARIMA model and a: .o:.and 0': represent the residual variances of the components. By taking the limit of the above expression with respect to the ratio of the component variances. he 41 showed that the relative gain decreases as the difference between the component variances increases. Nelson further analyzed the relationship to make the following conclusions. The gain will disappear as the forecast horizon increases because the component variances approach the residual variance of z(t). There will be no gain in efficiency if the component models are identical in form and have the same parameter values. Under these circumstances. 62- 6x I% 3 therefore the residual variances of the components sum identically to the residual variance of the aggregate series. Pierce (1975) derives the necessary and sufficient conditions under which the TF model will outperform the ARIMA model in a forecasting context. Begin with' the following models: q‘(B) x(J) I 9&(B) e(J) ( ( (B) ( ) g, B) y J) I B; U J y(J) I (w(B) /d(B)) x(J) +*V(B) a(J) where e(J). u(J). and a(J) are white noise series. Substituting for x(4) yields (a (BUG (an um a (w(B)B (B‘)/d(B) 91(3)) em Y Y x x + ‘0’ (B) a(J). 42 Consolidating the operators on e(J). the right hand side of the equation can be written as follows: X(B) e(J) +‘¥(B) a(J). Isolating u(J) produces u(J)I (“(8)9 (Blfi (B)! d(B)B (8)9 (B))h(J) x y X Y +( ‘l’ (B) fly(B)/9y (B) ) a(J) where "(B) is w(B)! wa and h(J) is e(J)! wb . The effect of the transformation is to insure that the first parameter of P(B) in the following equation- is - equal to one. Consolidating terms yields u(J) I P(B) e(J) + 0(B) a(J). The TF model will provide smaller single period mean square forecast errors if any. and only if all. of the following equivalent conditions hold: 1. P(B) of pin) are not identically 1 or zero. 2. X(B) is not equal to 9’(B) and neither of the components of u(J) vanishes. 3. For some k)0. the cross correlation between e(J) and u(J) is non zero. The above conditions imply that no improvement in predictive accuracy will be gained if the univariate models for x and y are identical. in both form and parameter values: the lag parameter is zero: and the cross correlation function 43 between the prewhitened series is not zero for some lag greater than zero. The models developed in this study will be examined with respect to the first condition. The estimated values for the model parameters will be inspected to see if the P(B) and 0(B) terms are identically one. The results of this inspection are reported in Chapter VI describing the results of the modeling process. As mentioned before. the arguments for the superiority of the TF model were developed assuming that the models are correctly identified and that the parameters are correctly estimated. In practice. sampling error will raise the possiblity that these assumptions will be violated. Indeed. the studies by Cheung (1977) and Manegold (1978) were unable to empirically show any consistent superiority of the TF model. 3-4 mm 'This chapter presents a discussion of the methodology used in the study. The notation for the ARIMA and transfer function models is presented. The three stages of model building ) identification. estimation. and diagnostic checking are described for both types of models. Arguments are presented which provide the conditions necessary for the TF model to provide superior forecasts relative to the ARIMA model. The-increased forecasting performance of the TF model diminishes as the forecast horizon increases. Chapter IV THE RELATIONSHIP BETWEEN CASH FLOW AND EARNINGS The previous chapter described the forecasting models used in this study. A prime question is whether or not the methodology is appropriate for the experimental design used in this study. That is. is there a relationship between the cash flow series and the earnings series which may be useful for forming the required prediction models? This chapter presents arguments that show it is plausible to expect that a transfer function may be formed between the cash flow and earnings series. The chapter begins by defining a set of terms. In order to simplify the notation. the tilde typically used to denote a. random variable has been deleted.' The cashflow and earnings variables are assumed to be random variables. Two cases are developed analytically which relate the earnings and the cash flow series as a transfer function. 4-1 NQIAILQN The following set of notation is used in the balance of this chapter: Time subscripts are denoted by t and J. They can be thought of as representing the end of an 44 45 accounting period. For the two flow variables. earnings and cash flows. the subscript denotes the value of the variable computed at the end of an accounting period. ‘t-J(It-J) is a function on It_J . the investment made in time t . The function relates an investment at time t-J to the cash flow at time t arising from that investment. The function need not be the same across. investments and is therefore subscripted to denote that it is related to an investment made at a specific point in time. A superscript of B is used to denote the function as cash from operations before tax. If A is the superscript. then the function is for cash from operations after taxes payable for the period. { ..Nt is the net amount of the accruals. inventories. and deferrals at time t with the exception of the deferred tax account. L is the productive life of an investment proJect. It is assumed to be known. Et is the accrual earnings from operations at time t. Mt is the cash earnings from operations at time t. .. 46 T is the amount of tax for period t. It is superscripted with an E or a C to represent the tax computed on the financial statement earnings or the tax computed on current taxable income respectively. B is the amount of depreciation for period t. It is superscripted with an E or a C to represent depreciation for financial reporting purposes or depreciation for tax purposes respectively. 4-2 9.6.35]. The purpose of the following analysis is to show that past observations of the earnings series may be related to the future observations of the cash flow series. For the time being ignore the effect of taxes on the two series. The current cash operating income can be viewed as the sum of the cash returns made from investments in past periods. That is Mt - E'sffl It_J . J=1 The earnings number can be viewed as the cash from operations number plus .the net change in accruals. deferrals. and inventories less the amount of financial accounting depreciation. Thus. earnings can be represented - 47 Assume that the firm has Operating characteristics such that N is proportional to M for the same period t. It is not unreasonable to think of sales on credit as having a fixed or fairly stable relationship to cash sales. Payables used to finance the inventory can be expected to increase as the level of inventory increases. Therefore. if the firm has a policy of keeping a fixed number of days supply of inventory then payables will .also vary with cash sales assuming a fixed relationship between credit and cash sales. Denoting the constant as p. leads to EtIMt+p(Mt-Ht_1)- a: . A‘maJor difference between cash flow and accrual earnings is the amount of depreciation expense. Since firms do not typically pay cash dividends in excess of earnings. depreciation can be viewed as a restriction on the. use of cash flow for dividends. The amount restricted can be invested in the firm or can be used to retire debt. Assuming that some of the cash flow restricted by the amount of depreciation is used for investment. depreciation expense in the current period should be related to future cash flows. If it is assumed that the cash invested is equal to the restriction on the use of the cash imposed by the current amount of depreciation. then investment can be represented as 48 Substituting into the expression for earnings and solving for investment. yields I I M + p(M - M ) - E . t t t t-l t Cash flow is a function of investment. Substituting. produces at: B, Mt 3:21 9'” (Mt_J + amt?J - M t_1_J) - Et_J ). From the above expression it is apparent that cash-flow can be represented as a function on past. cash flows and past earnings. By defining the cash flow return on investment function. fig” (It_ ). the expression can be rewritten to the form of a transfer function. Two assumptions regarding the return on investment function are required in order to develop a transfer function which has stable form and parameter values. 1. Assume that the investment made in period t has a life. L. which is a constant for investments made in all t. This assumption is required in order that the form of the transfer function remains constant. If the lives of investments proJects were allowed to vary significantly. then as time moves forward the current cash flow would be a function of a varying _. number of past investments. Therefore. current cash 49 flow would be a function of a varying number of past cash flows and earnings numbers. I 2. Assume that the cash flow return on investment function is the same for each investment package. That is. if the cash flow in time t resulting from an investment made at time t-1 is .S of that investment. then the cash flow in time t+1 resulting from an investment made at time t must also be .8 of the investment made at time t. This assumption is required so that the parameter values of the transfer function are stable. The effect of the above assumptions is to make the return on ‘investment function for each investment the same. Therefore. the subscript on the function can be removed resulting in the following relationship: L .MtI J3; f ("t-J + p(Nt-J - Mt-J-l ) - Et-J ). The above assumptions are not as unreasonable as they may appear on first reading. It must be kept in mind that the investment terms in the equations do not represent individual investments. They represent a package of investments made during a year. Therefore. the assumptions require that the return function be constant across these packages of investments. For the purpose of formulating the transfer function. "assume a firm with a positive rate of return. Define the 50 cash flow return on investment function such that the life of investment proJects is two periods. Let the return one period after the investment is made be equal to .8 of the investment and the return two periods after the investment is made be equal to .4 of the investment. Evaluating the return on investment functions at time t yields 4: (I )- .emt_ + .. .. t_1 pfl‘lt n ) E ) 1 -1 t-2 t-l and e (I t_2 ) - .4mt_2 + p(Mt_2 - N.t_3) - Et_2 ). By consolidating terms. the model can be written as This representation of the model is recognizable as the form of the transfer function presented on page 32. In this model. r I 3. s I 2. and b I 1. Inspection yields dlae8+P ”OI-e8 d2I.4+1.8p wlI.4 d.3I .4p b I 1. The expression for cash flow developed in this section indicates that earnings may be usefbl in predicting cash 51 flow. Two points can be noted about the model. I First. the assumption that investment equals depreciation can be relaxed without invalidating the model as long as there is a relationship between investment and depreciation. Second. if depreciation is small relative to earnings. then the earnings and cash flow become nearly identical. This means that the expression will reduce to a function solely on cash flow. Therefore. the amount of depreciation relative to earnings should be important in establishing a useful predictive relationship. This relationship is investigated by examining the forecasting performance of models for firms with high depreciation relative to earnings before depreciation. 4-3 QA§§2 The previous case ignored the effect of income taxes on the cash flow and earnings series. The difference in the tax amounts for the earnings series and the cash flow series can be substantial for expanding firms. This section adds the effect of taxes to the model previously developed. The same conditions are assumed for this analysis as were assumed in the development of the first model. In addition. it is assumed that the marginal tax rate is a constant denoted by r. Begin by defining the cash flow after tax as I. m - TC) - 2'. f“! . t ng t-J 52 The after tax earnings can be represented as - __ C __ ‘_ E__ (E 1B).; m T )t +p(Mt Mt_1) r(Dt 5t) E - D t . Substituting investment in time t for depreciation and solving for I yields It cm T)t+p(l'lt 191(1): at) (E TE) . Substituting investment into the expression for cash flow after tax yields L m - 1C )t - Z chm-TC)? - (E-TE) E ngcz J -r(Dt_; Dt_J). + p(Ht_ - M ) t-J J t-J-l s, Substituting with the return on investment function yields (.4 - Fit - .em - TC)t_1 - .404 - Tc)t_2 - E E .eus T >t_1 .4(E T >t_2 ' _ __ E __ C + .8( p(l‘1t_1 "t—Z) P(Dt-l Dt-l ) ) _ __ _. C + .4: p(Ht_2 Mb ) r(l§t_2 Dt_2 ) a. 3 The above equation shows that there is a relationship between cash flow after tax and earnings after tax. The model looks like a TF model with the last term representing part of the noise model. As with Case I. the parameter values can determined by inspection. They are d . .8 w 3".8 l O 53 d2.e4 ”lg—.4 b I l . Like Case I. as the depreciation approaches zero the difference between earnings and cash flow becomes negligible. The model then reduces to a function solely on cash flow or earnings. As mentioned before. the role of depreciation in the prediction model is investigated. 4.4 CHAPTER EQMflAR! This chapter presents two arguments which show that cash flows and earnings may be related such that a transfer function can be formed. Several assumptions were made in order to form the models. To the‘ extent that these assumptions do not hold in the real world. the validity of the models is suspect. It is not possible to make conclusions about the Joint effects of relaxing the assumptions. The research empirically tests the. Joint effects of removing the assumptions on the predictive ability of the TF model relative to the ARIMA model. Chapter V VARIABLE DEFINITIONS AND DATA GATHERING . This chapter presents a detailed definition of the variables used in the study. a description of the cash flow.surrogate. and a description of the data gathering process. Each of these topics is covered in a separate section . The topics are covered in the order indicated at the beginning of the chapter. 5.1 WEW The terms earnings and cash flow are broad terms open to many interpretations. This section of the chapter provides precise definitions for the terms as they are used in this study.’ First. the Justification for using variables classified as “from operations" is presented. This is followed by the definition of each variable. 5.1.1 justificatign £91,"ELQQ Operations" ggnigblg; Hithin the context of the stated obJectives for financial reporting. it appears that one of the purposes of earnings is to enhance the ability of financial statement users to predict enterprise cash flows. Hhat comprises a firms' earnings is the subJect of debate. One needs only to refer 54 55 to Appendix A of the Financial Accounting Standards Board’s discussion memorandum entitled onc Framework fig; WWMWt mum atatgmgngg and_Ihgin uggsgzgmgnt to appreciate this lack of consensus. Some would include the effect of all economic events. Others would exclude items not related to operations. Therefore. definitions must be derived for the variables used in this study. The outcome of a deterministic process can be determined exactly given the appropriate inputs. The operations of a business do not follow a deterministic process. They follow a stochastic process. Deviations from the underlying process occur due to unknown or uncontrollable variables. For instence. production schedules are not met due to strikes or natural disasters. The Box-Jenkins methodology is a technique for modeling stochastic processes. The observed series 'is treated as a sample from an infinite population of samples which could have been generated by the process. The form of the process and the value of its parameters are estimated from the sample data. Because the form of the stochastic process and the value of its parameters must be estimated from small samples. it is important that no extraneous data be imposed on the sample. Consider the following situation. A sample is obtained which is generated from a stochastic process. Now 56 add‘or subtract any amounts to several .observations in the series. Any estimates of the parameters of the underlying process will not agree with the estimates that would have been obtained from the true sample. Since the form of the model and the estimates of the parameter values are determined from an examination of the sample. the possibility of misspecifying the process increases. This problem would be minimized with large sample sizes. The writer contends that "from operations" numbers represent the realizations of some aggregate underlying process. To impose the random events of nonoperating items on the sample would increase the difficulty of identifying the process and therefore lead to model misspecification. Another argument for using variable; classified as “from operations" can be based on the accounting literature. 65.53.123.131 8.1mm 8.2mm 81- 9.2 published bu th! American Institute of Public Accountants states that: The ultimate distinction between operating income and charges and non-operating gains and losses ... has not been established. The former are generally defined as recurrent features of business operation. more or less normal and dependable in their incidence from year to year: the latter are generally considered to be irregular and ynggggigtghlg (emphasis added) . more or less fortuitous and incidental. The Accounting Principles Board (APB 19. para. 10) stated that. “the ability of an enterprise to provide working capital or cash from operations is an important factor in considering its financing and investment activities.“ 57 Accordingly. the APB required that either cash flow from operations or working capital from Operations be reported in the statement of changes in financial position. The computation of either amount requires that the effect of extraordinary items and most gains and losses be removed from net income. The total amount of reported income tax expense and the effect of any remaining items classified as other expenses or revenues are left in the “from operations" category. This opinion by the Accounting Principles Board was adopted by Financial Accounting Standards Board. It seems to indicate that "from operations" items are important. The models developed in Chapter III were based on "from operations" variables. These models indicate that it is reasonable to investigate the possiblity of a useful predictive relationship between earnings from operations and cash flow from operations. Given the above arguments. the variables used in the study are based on cash flow from operations and income from operations. 5-1-2 Eenninne Zanisbic Because earnings from operations includes tax-expense on items not related to operations. the variable used in this study is a modified version of earnings from operations. Logically. it seems reasonable to report an earnings from operations number which includes only the tax expense 58 associated with operations. The fact that all Of the income tax expense is reported in the "from Operations" category appears to be based on expediency rather than any theoretical foundation. Earnings from operations numbers were adJusted by the following method to remove the distortion caused by the inclusion Of the entire income tax expense in the variable. The amount of reported income tax expense was prorated between operations and "other items“ using the relative magnitudes of (operating income before taxes and pretax income. The adJustment assumes that the Operating and non-Operating items are taxed at the same marginal tax rate. For most gains and losses this is a valid assumption. The data. for the adJustment were taken from the quarterly COMPUSTAT tapes. 5.1.3 mammal}; The cash flow variable surrogated in the study is cash flow from operations with adJustments made for income tax. An adJustment identical to the adJustment used in modifying earnings from operations was used. to remove the effect of tax expense not associated with OperatiOns. Also. an adJustment for the change in deferred taxes was required in order to obtain the cash flow consequence of tax expense. Deferred taxes are the result of timing differences between accounting income and tax income in the recognition 59 of .revenues and expenses. Accounting Principles Board Opinion No. 11 states: Four types of transactions are identifiable which give rise to timing differences: that is. differences between the periods in which the transactions affect taxable income and the periods in which they enter into the determination of pretax income. Each timing difference originates in one period and reverses in one or more subsequent periods. 1. Revenues or gains are included in taxable income later than they are included in pretax income. For example. gross profits on installment sales are recognized for accounting purposes in the period of sale but are reported for tax purposes in-the period the installments are collected. 2. Expenses or losses are deducted in determining taxable income later than they are deducted in determining pretax accounting income. For example. estimated costs of guarantees and of product warranty contracts are recognized for accounting purposes in the current period but are reported for tax purposes in the period paid or in which the liability becomes fixed. 3. Revenues or gains are included in taxable income earlier than they are included in pretax accounting income. For example. rents collected in advance are reported for . tax purposes in the_ period in which they are received but are deferred for accounting purposes until later periods when they are earned. '4. Expenses and losses are deducted in determining taxable income earlier than they rare deducted in determining pretax accounting income. For example. depreciation is reported on an accelerated basis for tax purposes but is reported on a straight-line basis for accounting purposes. . 60 It is apparent that the source of deferred taxes stems from the reporting of operating items. Therefore. no allocation procedure is necessary with regard to the change in deferred taxes. All of the change in deferred taxes is included in cash flow from operations. 5-2 9655 ELQH.§!BBQQAIE Information is not available for a sufficiently long time to permit the computation of the cash flow variable as it is described in the previous section. Therefore. the computation Of a surrogate is required. The cash flow surrogate used in the study was computed by adJusting the earnings from operations variable for the effect of non—cash flow items included in that variable. Specifically. the amount Of depreciation and amortization for the quarter was added to the earnings variable. Also. one fourth of the annual change in deferred taxes was added to the variable on a quarterly basis. The surrogate represents the best estimate of cash flow from operations that an investor could make with publicly available information. As discussed in this section. it was not possible to ‘IdJUIt for the changes in accruals. deferrals. and inventories. The lack of this adJustment should not affect the ability Of the earnings variable to predict the cash flow surrogate. In referring to the hypothesized TF model developed on page 50. it can be seen that the failure to 61 adJust the cash flow variable by this factor in no way affects the validity of the model. Replacing the cash flow variable with its surrogate (S) and redefining the cash return on investment function in terms of S rather than M yields 8 + a as + e 48 B -e 8E -I 45 a t t-l t t The predictive relationship also holds in Case II when the appropriate substitutions are made. The balance of this section contains a discussion of the computation of the surrogate. The methodology requires large sample sizes in order to provide the statistical power necessary tO properly identify the fbrm of the model and to estimate the values of the parameters of the models. As explained in the Introduction. a study by Lorek and McKeown (1978) using quarterly data with univariate models has shown that thirty observations seems to be a minimum number of observations. Any differencing required to obtain stationarity reduces the effective number of observations in the sample. With respect to the TF models. Box and Jenkins (1970. pp. 374) mention that at least fifty observations ‘are required to obtain useful estimates of the cross correlation function. However. they also suggest that fifty Observations. is the minimum number of observations required for univariate modeling. Their fifty observation rule of thumb appears to 62 be. based on obtaining small standard errors of the estimators rather than any empirical evidence. No empirical study similar to the Lorek and McKeown study has been performed for the TF models. The use of annual data would expose the study to the risk that the process 'generating enterprise cash flows may have changed during the sample period. Also. changes in accounting standards over time would add to the difficulty of obtaining a meaningful surrogate. A pilot study performed with annual data indicated that reported financial data did not provide sufficient detail to compute an accurate cash flow number since non-cash flow items such as depreciation and amortization were not consistently reported over the required time period. For these reasons. it was determined that quarterly data would be used in the study. A statement of changes in financial' position or a detailed income statement and statement of financial position are required in order to compute the actual cash flow variable. ' Per APB Opinion No. 19. a statement of changes in financial position was required whenever a complete set of financial statements was published. However. complete quarterly financial statements were not required by the Securities and Exchange Commission until 1975. Therefore . quarterly statements of financial position or statements of changes in financial position were not available for the maJor part of the sample period. This 63 meant that detailed quarterly income statement data and annual statement of financial position data had to be relied on in order to obtain a sufficient number of observations. Four maJor items of information are required from the quarterly statement of financial position in order to compute the actual cash flow variable. They are the accounts receivable balance. the accounts payable balance. the amount of inventory. and the amount of deferred taxes. As mentioned before. the net change in accruals. deferrals. and inventories can be ignored without affecting the form of the hypothesized prediction models. An alternative to ignoring the amounts during the computation of the surrogate from available financial data would be to prorate the annual change in these accounts to the four quarters in the year. Since no Justification for this approach can be provided: and because the elimination of the amounts would have no maJOr effect on the prediction model developed in Chapter III. it was decided not to adJust for these amounts. The change in deferred taxes was assumed to be a function of time rather than a function of business activity in the period. This assumption is made on the basis that the timing ' difference which caused the deferral. reverses as a function of time rather. than a function of business activity in any one period. The timing difference due to the use of different depreciation methods for tax reporting and financial statement reporting is a good example of this 64 process. In preparing the interim financial statements. it is reasonable to expect that the annual amount Of depreciation would be divided equally 'among the four quarters. Therefore. the reversal of the timing difference should also be equal for all four quarters. For this reason. the annual change in deferred taxes was divided by four and used to adJust the quarterly earnings variable to a cash flow variable. 5.3 magmas The primary source of data for the study was the quarterly COMPUSTAT data base. This data base contains income statement information for the first quarter of 1962 through the third quarter of 1979. Because comprehensive income statement information was reported on a voluntary basis prior to the 1970 10K filing required by the Securities ... Exchange Commission. the data base is not complete for all firms. Statement Of financial position information is not available on the data base since it was not required by any authoritative body until 1975. The lack Of quarterly statement of financial position data for a maJor part of the sample periOd caused several surrogation problems with respect to the cash flow variable as previously described. In order to obtain the required information on the change in deferred taxes. it was necessary to use the annual COMPUSTAT data base for the \ period 1960 through 1980. 65 5.3.1 mam Table 1 provides a list of the data elements used to formulate the earnings variable and compute the cash flow surrogate. The name of the data element and the COMPUSTAT data base item number are presented. TABLE 1 DATAsELEMENTS DATA ELEMENT ITEM NUMBER Operating income before depreciation 21 depreciation and amortization . 5 pretax income 23 income taxes 6 deferred taxes(annual) 50 I. As mentioned previously. the data base is not complete for all firms because of the lack of mandatory reporting over the sample period. 5-3-2 MW Based on the work by Lorek and McKeown (1978). the Box and Jenkins (1970) suggestion that a minimum. of fifty observations be used in modeling. and the potential of lost Observations due to any required differencing. it was decided to use fifty Observations. for the modeling and identification portions of the research. An additional ten observations were used to test the forecasting ability of the models. The fifty Observation sample for model 66 identification and estimation purposes provides sufficient. statistical power while minimizing the problems associated with the underlying process changing over time. Based on this requirement and the data base available. it was decided to use the sixty observations beginning with the first quarter of 1964 and ending with the fourth quarter of 1978. Prior to investigating the contents of the data base. no information was available on the number of firms with complete data sets for the sixty observations beginning with the first quarter of 1964 and ending with the fourth quarter of 1978. A detailed search of the data base produced thirty firms with complete data sets and approximately another thirty firms with only one or two observations missing. The thirty firms with complete data sets were used in the research. As detailed in Chapter IV. the Hilcoxen signed-rank test was used to analyze the results Of the forecasting. This non-parametric test has a power-efficiency of 95% compared to the t-test for matched pairs. A sample size ’of thirty yields a power of .90 at an alpha level of .05 to detect a difference in forecasting accuracy of .6 of one standard deviation of the differences in forecasting performance. Table 2 provides of list of the firms used in the study. Because the firms used in the study do not represent a random sample. the results can not be generalized to all firms unless it can be shown that the sample firms are not TABLE 2 SAMPLE FIRMS ASARCO INC. _INCO LTD. HUDSON BAY MINING LOUISIANA LAND & EXP. BAYUK CIGAR AMERICAN SEATING INTERNATIONAL PAPER GREAT NORTHERN NEKOOSA UNION CAMP CORP. UESTVACO CORP. ALLIED CHEMICAL CORP. DUPONT HERCULES INC. UNION CARBIDE CORP. CITIES SERVICE CORP. PHILLIPS PETROLEUM CO. ROYAL DUTCH PETROLEUM CO. VULCAN INLAND STEEL CO. KAISER STEEL CORP. u S STEEL CORP. ‘ ALCOA. REYNOLDS METALS CATERPILLAR TRACTOR CO. MAYTAo‘ CO. CHRYSLER CORP. FORD MOTOR CO. OENERAL MOTORS CORP. EATON CORP. AROLLINS 68 different from the population of firms. Several industries are represented by the firms. No Obvious difference is apparent between the reporting and non-reporting firms. However. because no comprehensive theory exists which identifies all the factors that are important in establishing the predictive relationship between earnings and cash flow. it is not possible to fully investigate the relevant differences between the sample firms and the population. A search of the data base revealed that many Of the firms not used in the study began to report voluntarily prior to the 1970 requirements. Unfortunately. these firms did not report consistently until 1970. To the extent that the firms used in the study are systematically different from‘the non-reporting firms. the results of this study can not be generalized to all firms. 5-4 WW This chapter presented the definitions of the earnings and cash flow variables used in the study. Both variables were defined as being "from Operations“ numbers. A surrogate for the cash flow variable was required because of data limitations. Uith the exception of deferred taxes. the surrogate does not include the effect of the changes in accruals. deferrals. and inventories. The failure to adJust for these items is not expected to negate the hypothesized predictive relationship between earnings and cash flows. 69 The data collection process was explained. The lack of a random sample of firms placed limitations on the ability to generalize the results to all firms due to a self-selection bias present in the sample firms. Chapter VI MODELING AND FORECASTING This chapter presents the results of the modeling and forecasting. The statistical analysis of the forecasts is also presented. The first section of the chapter provides a description of the modeling process and the results Of this process. A discussion Of the forecasting process is presented in the second section of the chapter. Finally. the analysis of the results Of the forecasting is provided in the third section Of the chapter. I. 6.1. W The obJective of this phase of the research was to formulate an ARIMA‘ model and a TF model which were tO be used to forecast cash flow. In order to accomplish this obJective. it was necessary to formulate firm specific univariate models for the cash flow series and the earnings series. The univariate models based on cash flow were later used in the forecasting stage. The univariate modelt based on the earnings series were used to prewhiten the series when formulating the TF models. The following subsections of the chapter describe the univariate modeling and the multivariate modeling respectively. 70 71 6-1-1 mm For each firm and time series. eight baseline models were generated. These baseline models are models which have been suggested in the literature as being candidates for a general model which describes the time series of quarterly earnings. The purpose of generating the models was to provide a set of modeling statistics which would serve as a benchmark when testing the appropriateness of various models identified by examining the sample autocorrelation and partial autocorrelation functions for each firm.\ It was decided to use the baseline models with the cash flow series because no general, models have been formulated for this series. If the baseline models are improper. then a firm specific model for the cash flow series which provides better diagnostic statistics should be easily found. The eight baseline models are actually two versions Of four models. A deterministic trend constant was added to each of the four models in order to obtain the eight baseline models; The four models used in the study are: 1. The Foster model - (1.0.0) x (0.1.0) 2. The 2nd Foster model - (0.0.0) x (0.1.0) 3. The Hatts-Griffin model - (0.1.1) x (0.1.1) 4. The DrouréRozooe model - (1.0.0) x (0.1.1) Each of the eight models was generated for both time series of each firm. The Box-Pierce 0 statistic. a plot of the residuals. an autocorrelation function of the residuals. and 72 a partial autocorrelation ‘function of the residuals were available for each model. The next step in the modeling process was to identify the appropriate transformations required to obtain stationary series. A total of eight transformations and differencings were performed on the first fifty observations in each series. The following is a list of these differencings and transformations: I 1. no differencing - the orignal series 2. a first difference 3. a first seasonal difference with seasonal span of four 4. a combination of a consecutive difference and a seasonal difference with a seasonal span of four 5. no difference with a logarithmic transformation 6. a first difference with a logarithmic transformation ‘47.' a seasonal difference with a logarithmic transformation having a seasonal span of four 8. and a combination of a consecutive difference with a seasonal difference.span 'of four. using the logarithmic transformation. The first four transformations were selected based on the results of the studies which generated the baseline models. The logarithmic transformations were included because some economic series have a constant percentage change between observations. Hatts and Leftwich (1977) indicated that the 73 logarithmic transformation may be apprOpriate for annual earnings numbers. After selecting the appropriate differencing and transformation. an examination of the autocorrelation and' partial autocorrelation functions was performed. Based on the autocorrelation and partial autocorrelation functions. several potential models were identified for each firm and series. The parameters of these potential models were estimated. A plot of the residuals. the Box-Pierce 0 statistic. mean square error. and the autocorrelation function and partial autocorrelation of the residuals were used to analyze the appropriateness of the models given the baseline models. Ueing the procedures outlined in Chapter III. univariate models were selected for each of the two series for each of the sample firms. For thirteen of the thirty earnings models. the Brown-Rozeff model was selected over any hypothesized firm specific model based on the Box-Pierce 0 statistic. the autocorrelation function of the residuals. the partial autocorrelation function of the residuals. the distribution of the plot of the residuals. and the mean square error. None of the other general models wasselected over the firm specific models for the earnings series. Hith respect to the cash flow series. the Brown-Rozeff model was identified twelve times and the Griffin-Watts model was identified once. Appendix A presents the results of the 74 modeling process for the cash flow series and Appendix B presents the results of the modeling process for the earnings series. Appendices F and 0 contain the diagnostic statistics for the univariate cash flow models and the univariate earnings models respectively. The Box-Pierce statistic. the degrees of freedom. and the residual mean square are presented for each of the final univariate models. In addition. the probability of a Box-Pierce statistic equal to or greater than the reported statistic is given. If this prObability is .05 or less. the null hypothesis of no significant pattern in the autocorrelation function for the residuals must be reJected. This would indicate model inadequacy. Hith respect to the cash flow modelt. most of the models have Box-Pierce statistics which have probabilities of greater than .25 for a statistic of at least that large occurring. The model for Inland. Steel has the worst Box-Pierce statistic (16.414). The probability of a statistic that large or larger is .09. This is still safely within the acceptable range. Based on these statistics and inspection of the plots of the residuals. the univariate cash flow models show no signs of inadequacy. As mentioned in Chapter III. the Box-Pierce statistic is biased downward. The LJung-Box statistic does not have this bias._ However. the LJung-Box statistic is not computed by the software used in this study. Therefore. a solution to 75 the problem created by the bias is to manually compute the LJung-Box statistic when the Box-Pierce statistic approaches the reJection area. Because none of the cash flow models have a Box-Pierce statistic which approaches the reJection area. the LJung-Box statistic was not computed. Inspection of Appendix G shOws that none of the earnings models have a Box-Pierce statistic such that the probability Of a statistic that large or larger is less than .10. Inspection of the plots of the residuals revealed no model inadequacy. As with the cash flow models. the LJung-Box statistic was not computed. Examining the two sets of models on a firm by firm basis reveals two items of interest. In general. the residual mean‘ square is smaller on a firm by firm basis for the earnings models. This indicates that the earnings models "fit" the series better than the cash flow models. A second point is that for twenty-four of the thirty firms the univariate models for the cash flow series and the earnings series are identical in form. If the values of the parameters in the models are not different. this suggests that little advantage would be gained by forecasting with a multivariate model unless a lag exists between the series or the prewhitened series are cross correlated at some lag greater than zero. This issue is investigated by examining the results of the modeling process for the TF models. As mentioned in Chapter IV. if P(B) and 0(8) are not 76 identically 13 then the general superiority of the TF model should prevail. 6.1-2 mm mm A multivariate model which incorporated the cash flow series and the earnings in a forecasting model for cash flow was constructed for each firm. The procedure for accomplishing this phase of the research is explained in detail in Chapter III. A brief description of the process is presented here. The univariate models for the earnings series. ‘which are presented in Appendix B. were used to prewhiten the earnings and cash flow series. The cross correlations of the resulting series were then used to identify the order of the parameters and the lag. Estimates Of the parameter values in the transfer function were then made. Several models of the transfer function were identified and the parameters were estimated. The sampling error present in the cross correlation function makes it difficult to match the sample values to a theoretical function thereby creating the need for the testing of several hypothesized models. After the appropriate transfer function was selected. the noise model was formulated. This process involved examining the autocorrelation function of the residuals remaining after the application of the transfer function to the earnings series. Once the form of the model was identified. the parameters were estimated. 77 Appendix C contains the results of the ..multivariate modeling. The models presented in the appendix were used in the forecasting phase of the prOJect. Appendix H contains the diagnostic information for the TF models. Only the model for Eaton Corporation has a Box-Pierce statistic which indicates that the model may be inadequate. The probability of a statistic this large (17.879) or larger is .06. Since the statistic was close to the reJect area. the model was reviewed. The 8 statistic was 11.65. Comparison of this value with the Chi-Square distribution with 11 degrees Of freedom indicated that a value this large or larger has a probability of greater than .25 of occurring. Therefore. the actual transfer function portion of the model seems to be adquate. The modeling for the noise portion of the TF model was reviewed. No better model could be found. Therefore. the TF model for the firm was Judged to be adequate. A I“ . Inspection of the TF models and the univariate models reveals that all of the firms meet the conditions for multivariate model forecasting superiority. None of the firms have P(B) or 0(8), terms that are identically equal to one. The residual mean square values for the univariate cash flow models and the TF models were compared on a firm by firm basis. For 27 of the firms. the residual mean square was smaller for the TF model than the univariate model. 78 6-2 EQBEQAEIINQ Brown and Rozeff (1979) showed that the relative forecasting ‘ performance of time series models may change as the forecast horizon is varied. They examined the relative forecasting ability of several models over forecast lead times of one. five. and nine quarters. The research reported in this paper utilizes the idea of testing the models over several forecast horizons. For each time series. a total of sixty observations was available. The first fifty Observations were used in the modeling phase of the research. This left ten observations of the series on which to test the forecasting ability of the models. Using the univariate cash flow model and the TF model for each firm. a forecast was‘made for each of the last ten Observations in the series. This process resulted in a forecast made at origin 50 for each of the periods beginning with Observation 51 and ending with observation 60. The one-step-ahead through ten-step—ahead forecasts from the univariate cash flow model and the TF model were analyzed using the procedures described in the following section. 79 6-3 AMI-15.1.3 This section of the chapter presents an analysis of the results of the forecasting process. The error metrics used to evaluate the forecasting accuracy are described. A description of the statistical methods used in the study is presented. The statistical hypotheses are presented along with the results of the tests of these hypotheses. 6-3-1 mm: Three error metrics were used to evaluate the forecasting accuracy of the two types of models. . Absolute percentage error (APE) and percentage squared error (PSE) are two of the error metrics used in the study. These error metrics have‘ been used to evaluate forecasting performance in several studies reported in the accounting literature (Brown and Rozeff. 1979: Foster. 1977) and Lorek. 1979). The first Of these two metrics. “APE. assumes that the decision maker. has a linear loss function. The squared error metric assumes a quadratic loss function. . A formal description of the metrics is presented following an explanation of the third metric. A third metric. cumulative present value of the absolute error (CPVAE). was developed in an attempt to account for the “time value“ of the forecast error. For some investors or other users of forecast data. forecast errors Of equal magnitude may not have the same disutility if they are for 80 different lead times. That is an error of ten dollars in a forecast made ten-steps-ahead is not valued the same as an error of ten dollars in a forecast made one-step-ahead. Therefore. it was decided to discount each forecast error in a manner similar to computing the present value of a stream of cash flows. An arbitrary discount rate of 16% compounded quarterly is assumed. The metric has the advantage of providing a method of comparing the forecasting models as to their forecasting ability over all the forecast lead times in the event that one model is not consistently better over all forecast lead times. Table 3 presents a formal description of the metrics. with respect to the APE and PSE error metrics. a problem arises when the actual cash flow for period t approaches zero. This causes the value of the metric to become large. The values Of both of the metrics were examined for large errors caused by the aforementioned prOblem. In order to avoid having these large values of the error metrics place undue influence on the statistical interpretation of the forecast errors. errors greater than 100% were set to one. The statistical test used in this study ignores tied values. *Therefore. the effect of the transformation is to remove the observations :from the sample whenever a large error was encountered for forecasts from both models. Inspection of the forecast errors revealed that large errors occurred in pairs.~ That is. for a forecast of a particular cash flow APE(S) II( PSE(S) I ( CFt - FCFt-s (S) / CFt 10 81 TABLE 3 ERROR METRICS CFt - FCFt_s (S) ) / CFtl )2 CPVAE - Z PVAE(S) s=1 where: A 60 PVAE(S) - 2 ('CF - FCF (S) I 11—S ) / 1.045 t t-s t=s+50 APE(S) is the absolute percentage error for a forecast of S steps ahead PSE(S) is the percentage squared error for a forecast of 8 steps ahead CFt is the actual cash flow for period t FCFt_; (S) is the forecast of the cash flow made from period t-S for period t 82 number: both models produced large errors. This adJustment technique has been used by several researchers (Foster. 1976: Brown and Rozeff. 1979) when faced with similar situations. 6-3-2 Wati aneurysm Based on the above metrics a set of statistical hypotheses was developed. This set of hypotheses is centered on the omnibus null hypothesis that the multivariate model which incorporates the earnings variable is equal to Or worse in its ability to predict future cash flows when compared to the univariate model which is based only on the cash flow variable. The alternative hypothesis is that the multivariate model is superior to the univariate model in its predictive ability. In formulating the statistical hypotheses it was necessary to decide on a directional or nondirectional test of the data. Because prior research has not proven the superiority of multivariate models versus the univariate models it was decided to test the data using a nondirectional statistical hypothesis. This permits tests with sufficient power to detect situations where the univariate model is superior to the multivariate model. The directional test would not have the ability to detect this situation. . The APE and the PSE metrics were tested over each of the ten forecast lead times used in the study. This produces a 83 set of ten statistical hypotheses for.each Of Ch!!! metrics. The third metric. CPVAE. can only be tested on a meaningful basis across the sample firms which provides one statistical hypothesis. Rather than list all twenty-one statistical hypotheses. the following presents the three maJor null hypotheses with an indexing variable. 8. which is used to denote the lead time of the forecast. )40 (1.8) : APE(S.multivariate) I APE(S.univariate) H()(2.S) : PSE(S.multivariate) = PSE(S.univariate) HC,(3) : CPVAE(multivariate) I CPVAE(univariate) Ideally. parametric ANOVA would be used to test the above hypotheses. Unfortunately. the required assumption of homogeneity of variance can not be supported. This leads to the use of nonparametric tests. A nondirectional Nilcoxen signed-rank test was used to test the above set of hypotheses. Tate and Clelland (1957) state that: The signed-rank test is an excellent test. Its power is about 95 percent relative to the standard t test applied to normally distributed differences. It assumes continuous data. but is little affected by a moderate number of ties. 84 The test statistic includes the effect of the magnitude of the differences as well as the sign of the difference. A difference is computed for each pair of forecasts for each lead time. The absolute differences are then ranked. “The sum of the ranks is then computed for either the positive differences or the negative differences. whichever is smaller in number. The expected value is then subtracted from the resulting number and then standardized by the expected standard deviation. The result is a statistic which is compared to the standardized normal distribution. Brown and Rozeff (1979) used this test statistic in a similar experimental design. Based on a sample size of thirty. the power of the test is .90 at an alpha level of .05 to detect a difference in forecasting accuracy of .6 of one standard deviation of the differences in forecasting performance. 6-3-3 M1. Tables 4. 5. and 6 present the results of the tests of the statistical hypotheses. Table 4 presents the results of the tests related to the APE metric. The first column lists the lead time variable associated with the hypothesis. The mean and standard deviation of the error metric are presented for both models. The last column contains the level of significance of the test. Table 5 and Table 6 present the results of the tests related to the PSE and CPVAE metrics respectively. Their format is‘identical to that of Table 4 85 TABLE 4 TEST RESULTS APE - ALL FIRMS - ORIGIN 50 NILCOXEN SIGNED-RANK TEST OF MEDIANS FORECAST MULTIVARIATE UNIVARIATE LEVEL OF LEAD TIME MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 1 .2153 .2851 .2130 .2810 .5090 2 .2125 .2087 .2074 .2087 .6812 3 .2390 .2340 .2417 .2150 .9828 4 .2512 .2355 .2401 .2070 .3525 5 .3166 .2938 .2796 .2745 .1023 86 TABLE 4 (cont’d.) FORECAST MULTIVARIATE UNIVARIATE LEVEL OF LEAD TIME MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 6 .3022 .2662 .3040 .2724 .4874 7 .3547 .3104 .3539 ..2801 .8665 ‘8 .2455 .1573 .2194 .1368 .2942 9 .3111 .2664 .2935 .2571 .3931 10 .3406 .2570 .3115 .2403 .3044 87 TABLE 5 TEST RESULTS PSE - ALL FIRMS - ORIGIN 50 NILCOXEN SIGNED-RANK TEST OF MEDIANS FORECAST MULTIVARIATE UNIVARIATE LEVEL OF LEAD TIME MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 1 .1250‘ .2976 .1215 .2849 .4405 2 .0872 .1991 ' .0851 .1950_ .9393 3 .1100 .2124 .1031 .1992 .7672 4 .1167 .2162 . l .0991 . .1959 . .0962 5 .1837 .3085 .1510 .2980 .0247 99 TABLE'S (cont’d.) FORECAST MULTIVARIATE UNIVARIATE LEVEL OF LEAD TIME MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 6 .1599 .2739 .1642 .2919 .6570 7 .2199 .3341 .2012 .3009 .7639 9 .0943 .0919 w .0663 ~.O679 .3332 9 .1654 .2698 .1500 .2500 .5591 10 .1779 .2588 .1529 .2203 .3055 89 TABLE 6 TEST RESULTS CPVAE - ALL FIRMS r ORIGIN 50 HILCOXEN SIGNED-RANK TEST OF MEDIANS MULTIVARIATE UNIVARIATE ‘ LEVEL OF MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 407.147 926.321 201.914 230.699 .1714 With respect to the set of hypotheses regarding the APE’ metric. the null hypothesis can not 'be reJected at the .05 level for any Of the forecast lead times. There appears to be no pattern in the direction Of the differences in the metric value across forecast lead times. .For the tests on the PSE metric. only the null hypothesis for a forecast lead time of five can be reJected at the .05 . level. The direction of the difference favors the univariate model. This result was not expected based on the discussion presented in Chapter 3. The multivariate model should not perform worse than the univariate model provided that sampling error has not caused a misspecification of the models. For the CPVAE metric. the null hypothesis was not reJected. Care should be exercised in interpreting the mean values for the CPVAE statistic. Because the firms in the sample are different sizes as measured by the level of 90 earniRgs. differences in forecasting accuracy of the same percentage yield different absolute magnitudes in terms of dollars. This means that large firms tend to influence the mean value of the metric more than small firms do. An inspection Of the actual values of the metric revealed that the multivariate models produced smaller metrics for 14 of the firms. The lack of statistically significant results could be a function of the actual power of the tests. The power of the test for the one-step-ahead forecasts utilizing the APE metric was computed. An estimate of the standard deviation of the difference between the values of the APE metric for each model was made from the forecast data. This sample value (.111) was used with the power tables for the t-test of matched pairs to determine the power of the test. A power-efficiency Of .95 was used for Nilcoxen signed-rank test. The estimated power of the test is .9 at an alpha of .05 to detect a difference of .06 between the median of the APE values for 'the univariate models and the median of the APE values for the TF models. In an effort to increase the power of the test. a new set of forecasts was generated from the models using the procedures described in the following paragraphs. The forecasting procedure involved generating forecasts beginning with the information available in the first fifty observations of each time series. From this time period it 91 was possible to generate a forecast for each of the ten observations left in the time series. Next. the period from which the forecasts were being made was moved forward one quarter leaving nine observations on which forecasts could be tested. The origin of the forecasts was moved forward one quarter at a time and forecasts were generated for each quarter remaining in the time series. This procedure produced a set of forecasts consisting of one ten-step-ahead forecast. two nine-step-ahead forecasts. three eight- step-ahead forecasts and so forth down to ten ‘one-step- ahead forecasts. Before the forecasts were made at each change in the forecast origin. certain adJustments were made to the models. First. the earliest observation in the cash flow series was dropped and the observation of the series which provided the new forecast origin was added to the data used in the modeling stage of the research. Then the parameters of the univariate cash flow model and the TF model were reestimated. This procedure kept the number of observations used to estimate the parameter values constant as the forecast origin was moved forward. Several alternatives exist to the procedures described in the previous paragraph. First the values for the parameter estimates could have been left constant. Research by McKeown and Lorek (1978) suggests that forecasting ability can be improved by reestimating the parameter values as the 92 forecast origin is changed. Another alternative would have been to remodel at every forecast origin change. This alternative was ‘ reJected because the results of the previously mentioned study showed that no significant change in accuracy results from this procedure over several changes in origin. With respect to the dropping of the earliest Observation in the series. it was decided to use the procedure outlined above rather than to bias the results in favor of more precise parameter estimates as the origin was moved forward. A The procedure described above has. a potential biasing problem with respect to the forecasts from the TF models. Because the lag term .b . in the transfer function portiOn of the model is zero for all models. forecasts of the earnings variable are required in order that forecasts can be generated from the TF models. These forecasts are automatically generated by the software from the prewhitening model. However. the values Of the parameters in the prewhitening model are not automatically reestimated as the forecast origin is changed. Therefore. there is a slight bias against the accuracy of the forecasts of the TF models. Complete reestimation of the earnings models and complete remodeling of the TF models at each forecast origin would be required in order to avoid this potential problem. Because the extent of the bias could not be determined and the reason for the new forecasts related. to increasing the 93 power of the test. the comprehensive remodeling was not. performed. Tables 7. 8. and 9 present the results of the tests with the increased sample size. Table 7 presents the results of the tests using the APE metric. Tables 8 and 9 present the results of the tests using the MSE and CPAVE metrics respectively. With respect to the set Of hypotheses regarding the APE metric. only the null hypotheses for forecast lead times of two. three. and five can be reJected at the .05 level. The direction of the difference in the metric values for the multivariate and univariate models favors the univariate model in all cases. The same relationship holds for the tests of the set of hypotheses related to the PSE metric. Null hypotheses having forecast lead times of two. three. four and five can be reJected at the .05 level. The null hypothesis for the CPVAE could not be reJected at the .05 level and the direction also favored the univariate model. The direction of the differences in the metric values is the opposite of the posited direction. NO information should be lost by adding the additional variable to the model. Apparently the bias against the forecasts from the TF models contributed to these results. 94 TABLE 7 TEST RESULTS APE - ALL FIRMS - ALL ORIGINS NILCOXEN SIGNED-RANK TEST OF MEDIANS NFORECAST MULTIVARIATE LEAD TIME MEAN STD. DEV. 1 .2054 2 .2311 3 .2374 ’4 .2575 5 .2877 .2431 2461 .2386 .2646 .2661 UNIVARIATE MEAN STD. DEV. .1940 .2380 .2143 .2398 .2228 .2317 .2414 .2403 .2608 .2425 LEVEL OF SIGNIFICANCE .1490 .0034 .0075 .0899 .0307 95 TABLE 7 (cont’d.) FORECAST MULTIVARIATE UNIVARIATE LEVEL OF LEAD TIME MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 6 .2826 .2530 .2723. .2288 .8450 7 .2917 .2478 .2870 ..2270 .7000 8 .2800 .2059 .2663 .2113 .7800 9 .3196 .2537 .3051 .2537 .4409 10 .3406 .2570 .3115 .2403 .3044 96 TABLE 8 TEST RESULTS PSE - ALL FIRMS - ALL ORIGINS HILCOXEN SIGNED-RANK TEST OF MEDIANS FORECAST MULTIVARIATE UNIVARIATE LEVEL OF LEAD TIME MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 1 .1011 .2344 .0940 .2232 .1932 2 .1137 .2405 .1032 .2312 .0017 3y .1130 .2310 .1031 .2225 . .0014 4 .1360 .2653 .1157 .2330 .0256 5 .1532 .2706 .1265 .2403 .0157 97 TABLE 9 (cont’d.) FORECAST MULTIVARIATE UNIVARIATE LEVEL OF -LEAD TIME MEAN STD; DEV. MEAN STD. DEV. SIGNIFICANCE_ 6 .1434 .2515 ' .1261 .2260 .5166 7 .1460 .2493 .1335 _.2240 .9355 .9 .1203 .1910 .1151 .1939 .9554 9 .1654 .2533 .1563 .2416 .5000 10 .1900 .2599 '.1529 .2203 .3055 98 TABLE 9 TEST RESULTS CPVAE - ALL FIRMS - ALL ORIGINS NILCOXEN SIGNED-RANK TEST OF MEDIANS MULTIVARIATE UNIVARIATE LEVEL OF MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE. 448.084 998.646 445.180 1000.993 .5039 6.3.4 Contrglling fgr Depreciation Chapter III presented two models which indicated that depreciation may be an important variable in establishing a relationship between earnings and cash flow which is useful for predicting cash flow. Therefore. firms were examined with respect to this variable. The percentage of ' depreciation to operating income before depreciation was computed based on the last ten observations. in the series. Thirteen firms had percentages of 35% or greater. Kaiser Steel was not considered to be part of the large depreciation set even though the depreciation percentage was 175%. The large percentage was caused by income which was near zero or negative for the computation period and thus was felt to be a function of the small denominator rather than the true relationship between depreciation and operating income before depreciation. 99 A list of firms and depreciation percentages is presented in Appendix D. The firms with high depreciation percentages were reexamined using only the forecasts from origin 50 so as to avoid the biasing problem. Table 10 presents the results of these tests for the APE metric. The results of these tests are quite encouraging. The test for one-step-ahead forecasts is significant at the .06 level and is in the direction of the multivariate models. In addition. the direction of the differences supports the multivariate models for lead times two. three. and six. Table 11 presents the results of the tests using the PSE metric for the high depreciation set of firms. As with the tests using the APE metric. the direction of the difference in forecast errors favors the multivariate models for the lead times one. two. and three. The test for the one-step-ahead forecast is significant at the .04 level. .Ndne of the other tests were significant at the .05 level. The result of the test using the CPVAE metric is reported in Table 12 . No significant difference was found. Based on Nelson (1975) it is to be expected that the improvement in forecasting accuracy exhibited by the TF models would decrease as a function of lead time. The results of the tests utilizing the APE and PSE metrics follow this expected pattern for the first three lead times. After the first three lead times. the direction of the a difference appears to follow no pattern. 100 TAhLE 10 TEST RESULTS APE - HIGH DEPRECIATION - ORIGIN so NILCOXEN SIGNED-RANK TEST OF HEDIANS FORECAST MULTIVARIATE UNIVARIATE LEVEL OF LEAD TIME MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 1 .2213 .2714 .2532 .2811 .0597 2 .2253 .1885 .2328 .1900 .8068 ‘3 .2000 .1473 .2195 .1545 .4631 4 .2515 .1648 .2395 " .1277 A .9165 5 .2783 .2346 .2492 .2396 .2094 101 TABLE 10 (cont’d.) FORECAST MULTIVARIATE UNIVARIATE LEVEL OF LEAD TIME MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 6 .2855 .2410 .3232 .2488 .1961 7 .4668 .3897 .4596 .3665 .7989 8 .2550 .1623 .2222 ‘.1389 ' .9800 9 .3453 .2934 .3289 .2557 .6949 10 .3244 .2663 .3083 .2247 .8613 102 TABLE 11 TEST RESULTS PSE - HIGH DEPRECIATION - ORIGIN 50 NILCOXEN SIGNED-RANK TEST OF MEDIANS FORECAST MULTIVARIATE UNIVARIATE LEVEL OF LEAD TIME MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 1 .1171 .2817 .1369 .2914 .0409 2 .0835 .1440 .0876 .1282 .6661 ‘3 .0600 .0905 .0702 .0956 .1842 4 .0883 .1108. . .0724 .0636 .6566 5 .1284 .2652 .1151 .2681 .0995 103 TABLE 11 (cont’d.) FORECAST MULTIVARIATE UNIVARIATE LEVEL OF LEAD TIME MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 6 .1350 .2149 .1617 .2344 .1916 7 ‘.3580 .4502 .3354 ..4108 .4446 8 .0894 .1050 .0673 ..0682 .8753 9 .1987 .3134 .1685 .2668 .8445 10 .1708 .2314 .1417‘ .1550 .9165 104 TABLE 12 TEST RESULTS CPVAE - HIGH DEPRECIATION - ORIGIN 50 NILCOXEN SIGNED-RANK TEST OF MEDIANS MULTIVARIATE UNIVARIATE LEVEL OF MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 324.506 445.785 261.237 239.275 .5525 These results indicate that depreciation may be an important factor in providing the necessary relationship between earnings and cash flows. An inspection of the models,for the high depreciation firms shows- no particular pattern in the TF models which would distinguish them from the other models. The effect of the depreciation must therefore be in the variables rather than the models. As shown in Chapter III. the TF model approaches an ARIMA model on cash flow as the difference between earnings and cash 'flow grows smaller. Examination of some of the TF models indicates that "if there is little difference between the series. the models reduce to the concurrent value of earnings plus some noise. In an effort to increase the power of the tests for the firms with large depreciation percentages. the biased set of forecasts was used to test the hypotheses for the APE and PSE metrics. The results of these test are reported in Tables 13 and 14 . 105 TABLE 13 TEST RESULTS APE - HIGH DEPRECIATION - ALL ORIGINS NILCOXEN SIGNED-RANK TEST OF MEDIANS UNIVARIATE LEVEL OF MEAN STD. DEV. SIGNIFICANCE FORECAST MULTIVARIATE LEAD TIME MEAN STD. DEV. 1 .2217 ' 2 .2596 3~ .2672 4 .2974 .2622 .2650 2622 .2885 .2888 .2274 .2432 .2550 .2848 .2892 .2617 .2601 .2570 .2618 .2691 .4950 .1596 .6220 .7215 .9941 106 TABLE 13 (cont’d.) FORECAST MULTIVARIATE UNIVARIATE LEVEL OF LEAD TIME MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 6 .3100 .2848 .3099 .2599 .0925 7 .3245 .2922 .3157 ‘.2704 .2041 8 .2858 .2053 .2624 .2098 .7514 9 .3168 .2535 .2948 .2421 .7776 10 .3244 .2663 .3084 .2247 .8613 107 TABLE 14 TEST RESULTS PSE - HIGH DEPRECIATION - ALL ORIGINS NILCOXEN SIGNED-RANK TEST OF MEDIANS FORECAST MULTIVARIATE UNIVARIATE LEVEL OF LEAD TIME MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 1 .1174 .2565 .1196 .2491 ' .3016 2 ' .1370 .2621 .1263 .2526 .1457 3 .1394 .2638 .1304 I .2582 .5986 '4 .1708 .3052 .1489 .2673 .6532 5 .1754 .3043 .1551 .2759 .9184 108 TABLE 14 (cont’d.) FORECAST MULTIVARIATE UNIVARIATE LEVEL OF LEAD TIME MEAN STD. DEV. MEAN STD. DEV. SIGNIFICANCE 6 .1759 .2906 .1626 .2646 .1283 7 .1890 .3098 .1714 ..2720 .1153 8 .1228 .1855 . .1118 .1815 .5871 9 .1622 .2386 .1432 .2158 .9250 10 .1708 .2314 .1418 .1550 .9165 109' None of the tests utilizing the biased forecasts were significant at the .05 level. The direction of the difference in metric values tend to favor the univariate models. Again. the effect of the bias appears to have outweighed the effect of the increased power. 6.3.5 Matthew The results reported in the previous section are a function of several variables. That is. the results can not be attributed only to the relationship between cash ~flow and earnings. Other factors in the design may have contributed to not finding a general improvement in the ability to forecast cash flows when the information in the earnings series was added. This section of the chapter presents a discussion of the role which various items in the research design may have played in affecting the results of the ‘experiment. Because it was necessary to use a surrogate for the cash flow variable. the true relationship between cash flow and earnings may not have been captured in the forecasting models. The surrogate used in the study represents the best estimate of the firm’s cash flow that could have been made with publicly available information. With the exception of .deferred taxes. the computation of the cash flow surrogate ignores the net change in deferrals. accruals. and inventories. However. the difference between the cash flow 110 variable and the earnings variable caused by these items may be negligible compared with the differences caused by depreciation and deferred taxes. In addition.. the models developed in Chapter IV indicate that the surrogate can be substituted for the actual cash flow variable without affecting the hypothesized prediction model. Therefore. it may be argued that the surrogate’s impact on the overall results is relatively minor. The methodology used in an experiment may affect the ability to detect a hypothesized relationship. The Box-Jenkins methodology used in this research is a state of the art forecasting technique. Lorek. McDonald. and Patz (1976) showed that the methodology was able to produce better forecasts of quarterly earnings than managers were able to produce. Thus. the accuracy of the forecasting models developed with the technique should be acceptable in relation to ad hoc models. As with all statistical forecasting techniques. a past series of data must be used to establish the model. Also. an assumption is required that the relationships that occurred in the past will continue to otcur in the future if the prediction model is to be of any use. As larger numbers of past observations are used to estimate the models. the possibility that a fundamental change to the process generating the series has occurred increases. This would cause the models to be incorrectly specified. Conversely. 111 the smaller the number of observations used to estimate the models. ' the less precise are the estimates. The 50 observations used for model identification and parameter estimation approaches the lower limit of the generally recognized sample size required by the methodology. This minimizes the problems associated with changes in the process during the estimation period. with regard to the assumption that the past relationship will hold in future. one must look at the period used to test the forecasting models. The models were tested over the period beginning with the third quarter of 1976 and ending with the last quarter of 1978. This was a period of instability for many of the industrial firms in the sample. The effect of this instability may hav; been a fundamental change in the earnings and cash flow generating process. By examining the forecast errors. it is possible to make some statements about the adequacy of the models. For one-step-ahead forecasts. the forecast errors were roughly 22% of the actual values. A study by Brown and Rozeff (1979) which used quarterly earnings had forecast errors which were 32% of the actual values. Their forecasts were for one-step—ahead periods in the years 1975 through 1976. For similar periods. the forecast errors for the models developed in this dissertation produced smaller forecast errors._ This may indicate that the models are quite adequate. The diagnostic statistics for the models also point in this direction. 112 Chapter IV contains the development of two models which show that there should be a relationship between earnings and cash flow which can be expressed in the form of a TF model. These models were constructed based on assumptions regarding the role of depreciation in establishing the amount of investment undertaken by the firm and the form of the return on investment function. It is not possible to determine the validity of the assumptions with available data. One purpose of the research was to empirically investigate the form of the relationship between earnings and cash flows. The result of that investigation is reported in Appendix H. The models all meet the conditions put forth by Pierce (1975) for the superiority of the TF models compared to the univariate model‘. That is. P(B) and 0(8) are not identically one. The results of the statistical tests performed on the high depreciation set of firms for forecasts from origin 50 provide encouraging results. As reported earlier the tests for the one—stepFahead forecasts were significant at the .06 and .04 levels for the APE and PSE metrics respectively- In addition. the direction of the tests favored the TF models for the next two lead times. The power of these tests was low as the number of observations was only 13. The trailing .off of the superior performance by the multivariate models is expected based on the arguments in Nelson’s 1975 paper. Given the low power of the test and the aforementioned 113 results. further research on the predictive relationship between earnings and cash flow should be performed as larger data sets become available. Chapter VII SUMMARY. CONCLUSIONS. AND RECOMMENDATIONS A summary of the research reported in this dissertation and a set of conclusions and recommendations drawn from the research are reported in this chapter. A section of the chapter is devoted to each of these topics. 7-1 51155631 Chapter I presented the motivation for the reported research and the specific research question. The prime motivation for the research was the assertion by the ‘Financial Accounting Standards Board made in its Statement of Financial Accounting Concepts No. 1 entitled 914g£11xg1 qt Eingngigl ngthan‘gy Busing11_fintgngniggg regarding the usefulness of accrual earnings numbers for predicting enterprise cash flows. Given the cash basis of accounting as a base level of information. the research question addressed by the study is : does the addition of the earnings number from the accrual accounting model to the information set provided by the past enterprise cash flows permit better predictions of future‘enterprise cash flows than predictions made from past enterprise cash flows. 114 115 The research does not attempt to address the cost-benefit issue raised by Beaver and Demski. Nor does the research address the form of communication issue. The research addresses the issue of the appropriateness of the accrual accounting model given the financial reporting obJectives rather than appropriateness of the model given other obJectives or uses of accrual accounting information. In Chapter II a survey of the literature concerning the forecasting and time series properties of various income measures was presented. The survey was divided into three areas: properties of annual income numbers. quarterly income number forecasting. and forecasting of enterprise cash flows. The annual accounting number studies illustrated the use of the Box-Jenkins methodology in the accounting literature and provided several philosophies on the importance of forecasting variables. Four general models of the quarterly earnings process were identified in the review of studies involving quarterly accounting numbers. These general models were used in\this research as baseline measures of model adequacy when building the firm specific models. A review of the accounting studies which dealt with forecasting enterprise cash flows indicated that little had been done in this area. A study by Cheung (1977) attempted to forecast cash flows by using multivariate models based on earnings components. The study used cash flow to securities 116 holders as the cash flow measure rather than cash flow from recurring operations as is used in the study reported in this dissertation. The Cheung study was not able to show superior results for the multivariate model as compared to the univariate model. A study by Manegold (1980) in which he forecasted earnings with multivariate models based on earnings components was also unable to show the superiority of the multivariate model. These two studies point to the lack of empirical proof for the theoretical superiority of multivariate models over univariate models for predicting accounting numbers. Chapter III presents an explanation of the methodology used in this research. It was intended to introduce the notational conventions to the reader who is unfamiliar with the Box-Jenkins methodology. A description of the model building process was presented in three stages: model identification. parameter estimation. and diagnostics.‘ A description of the forecasting procedure was presented. The fourth chapter presented an analytic argument for the existence of a predictive relationship between earnings and cash flows. Two models were constructed which indicate that depreciation and deferred taxes may be important factors in any predictive relationship between earnings and.cash flow. Chapter V presented the definitions of the variables used in the study. The earnings variable was defined as earnings from operations adJusted for tax expense from nonoperating 117 items. The cash flow variable was cash flow from operations. The variable was surrogated by adding depreciation and the change in deferred taxes back to the earnings variable. The data was taken from the quarterly COMPUSTAT data base for sixty observations beginning with the first quarter of 1964. Thirty firms had complete data sets for the purposes of this study. The sixth chapter presented the results of the modeling. the forecasting. and the testing of the statistical hypotheses. Thirteen of the univariate models for the cash flow series were identified as the Brown-Rozeff model and one was identified as the Griffin-Natts model. For the univariate models of the earnings series. thirteen models were identified as the Brown-Rozeff models. Twenty-four sets of univariate models were identified to have identical form. Forecasts were made of the cash flow variable for each firm with both the univariate and multivariate models. The forecasting procedure involved generating forecasts beginning with the information available in the first fifty observations of each time series. From the origin at time fifty it was possible to generate a forecast for each of the ten observations left in the time series. The forecast origin point was then moved forward one period and forecasts were made for the remaining nine observations. The procedure of shifting'the origin and forecasting was continued until observation sixty was reached. The parameters of the 118 ‘multivariate and the univariate models were reestimated each time the forecast origin was changed. Three error metrics were used to evaluate the forecasting accuracy of the univariate and multivariate models. Two of the metrics. the absolute percentage error and the percentage squared error. have been used.in several prior studies. A third metric was developed for this study in order to provide a test of the models over all ten forecast lead times. This metric discounted the mean absolute forecast error for a firm for each forecast lead time. The discounted means were then summed for each firm given the model type. The resulting number. the CPVAE. was tested across firms. Q 7-2 W The null . hypothesis of no difference in forecasting performance was tested for each forecast lead_time with forecasts made from origin 50. Uith respeét to the set of hypotheses regarding the APE metric. 1 none of the null hypotheses could be reJected at the .05 level. The same situation held for the test of the hypotheses using the PSE and CPVAE metrics. A A Depreciation was shown to be an important variable in the TF model for cash flow. Therefore. firms were examined with respect to this variable. The percentage of depreciation to operating income before depreciation was computed based on 119 the last ten observations in the series. Thirteen firms had percentages of 35% or greater. Table 10 presented the results of these tests for the APE metric. The test for one-step-ahead forecasts was significant at the .06 level and was in the direction of the multivariate models. In addition. the direction of the differences supports the multivariate models for lead times two. three. and six. Table 11 presents the results of the tests of the hypotheses for the PSE metric. The test for a forecast lead time of one was significant at the .04 level. The null hypothesis for the CPVAE metric could not be reJected at the .05 level. Therefore. depreciation may be an important variable in establishing a useful transfer function relationship between earnings and cash flows. An examination of the TF models gave no insight into how the amount of depreciation affected the models. In an effort to increase the power of the tests. the sample of forecasts was increased by moving the forecast origin forward. The values of the parameters in the univariate cash flow model and the TF model were reestimated each time the forecast origin was moved forward. This procedure resulted in forecasts which were biased in the favor of the univariate models because the parameters of the earnings models could not be reestimated without remodeling the TF models. The earnings model supplied forecasts used in the TF models. The results of the tests with the 120 increased sample sizes are reported in Tables 7 . B. 13. and 14 . With respect to the set of hypotheses regarding the APE metric. only the null hypotheses for forecast lead times of two. three. and five were reJected at the .05 level. The direction of the difference in the metric values for the ‘multivariate and univariate models favored the univariate model in all cases. The same relationship held for the tests of the set of hypotheses related to the PSE metric. Null hypotheses having forecast lead times of two. three. four and five were reJected at the .05 level. The null hypothesis for the CPVAE could not be reJected at the .05 level and the direction also favored the univariate model. The direction of the differences in the metric values was the opposite of the posited direction. No information should be lost by adding the additional variable to the model. These results are felt to be a function of the bias in the forecasts. l I In summary. the multivariate models and the'univariate models provided forecasts which were not statistically different. When the firms were partitioned by the J percentage of depreciation to operating income before depreciation.“ the null hypothesis could be reJected at the .06 (APE) anfl the .04 (PSE) levels for one step ahead forecasts. The direction of the difference favors the multivariate model for forecast lead times of two and three. 121 .Therefore. the study is able to provide some support for the contention that accrual accounting earnings are useful for predicting enterprise cash flows. 7.3 M TA The interpretation of the results of this study is subJect to several limitations. These limitations are discussed in this section. The results of this study can not be generalized to the population of all firms. The data used in the study suffers from self-selection bias. Few firms .reported consistently over the time period from which data was drawn. Therefore. it was not possible to take a random sample of firms from which to gather data. The terms cash flow and earnings have several definitions. Therefore. it was necessary to define these terms for the purpose of this study. To the extent that the variables were misspecified. then the results of the study must be questioned. A misspecification would manifest itself in results which showed no difference in forecasting ability between the models. Since a difference in the correct direction was obtained. this appears to of minor concern. Because of the lack of complete financial reports for the time series examined by the study. it was necessary to use a surrogate for enterprise cash flow. with the exception of 122 deferred taxes. the effect of the change in accruals. deferrals. and inventories was ignored in computing the surrogate from financial statement information. This was necessary due to the lack of detailed statement of financial position data. The surrogate represents the best estimate of enterprise cash flow that could have been with publicly available information. The relationships developed in Chapter IV indicate the this omission should not affect the predictive relationship between the earnings and cash flow. 7-4 W Based on the research reported in this dissertation several recommendations can be made for further research. The promising results for the firms with‘ high percentages of depreciation leads to recommending that further research be done to identify other variables which may enhance the predictive relationship between earnings and cash flows. This research should center on the variables which restrict use of current cash flows. such as loan covenants. The reported study used a cash flow surrogate because of the lack of reported data for a long enough time span. It is recommended that the study be replicated using the variables identified in this study when sufficient reported data becomes available to eliminate the surrogation problem. Finally. when sufficient data becomes available. research should be performed in order to identify a possible general 123 model of enterprise cash flow. This line of research may answer questions'as to the theoretical support for the superiority of the multivariate model compared to the univariate model. If the univariate models for earnings and cash flows are identical. little advantage may be gained from using the multivariate model based on cash flow and earnings to forecast enterprise cash flows unless there is a lag between the series or the impulse response weight is not zero for some lag greater than zero. APPENDICES 124 APPENDIX A UNIVARIATE MODELS - CASH FLOW SERIES ASARCO INCO HUDSON BAY LOUISIANA BAYUK AMERICAN SEATING INTERNATIONAL PAPER GREAT NORTHERN UNION CAMP WESTVACO ALLIED CHEMICAL DUPONT HERCULES UNION CARBIDE CITIES SERVICE PHILLIPS ROYAL DUTCH VULCAN INLAND STEEL KAISER STEEL (1-B)CFt = (-.6188)at (l-B)CFt = at 4 4 (1-.8283)(1-B )CFt = (l-.BOOB )at (l-B)CFt = .673 + (l-.43133)at L1-.605 + .33432)CFt = .464+at (1-.4923)(1-a‘)crt (1-.864B4)at (l-B)(l-B4)CFt = (1-.81134)at 4 (1-.3888 )(1-B)CFt - at (1-.357B4)(1-B)CFt - (1-.44233)+.t+.531 c1-a)(I-a‘)crt - (1-.79334).t (l-B)CFt = (l-.454B)at (1-.4493 + .3651‘32M1-mcrt = at 4 4 (l-.804B)(1-B )CFt ‘ (1-.397B )at (l-.4088)(1-B)CPt = at (1-.50134)(1-B)crt = (1-.294B)at (l-B)C1"t ‘ (l-.399B)at + 2.528 ' 3 (l-B)CPt = (1-.6598 )at 4 _ 4 L1-B(1-B )crt — (1T'3293 )at '_(1-.5393)(1-a4)c1='t = (1-.32934)at (1-B)CF£= (1.549B)at 125 APPENDIX A (cont ' d. ) u. s. STEEL (l-.767B)(1-B4)CFt = (l-.852B4)at 4 4 ALCOA (l-.830B)(1-B )crt = 41-.3533 )at REYNOLDS (l-B)(1-B4)CFt = (1+.54os)(1-.83034)at 4 2 CATERPILLAR 41-.4943 )(I-Emrt = (1-.47GB )at 4 4 MAYTAG (l-.SZlB)(1-B )crt = (1-.esoe )at 4 4 CHRYSLER (1'- . 6463) (l-B )CFt = 1- . 6958 )at i 4 4 roan (l-.BSOB)(1-B )crt = (1-.899B )at GENERAL morons (1-.6063)(1-E4)crt = (l-.77634)at 4 4 EATON (l-.84lB)(1-B )crt = (1-.507B )at RDLLINS (1-34)crt = .515 + a 126 APPENDIX B 4‘ UNIVARIATE MODELS - EARNINGS SERIES ASARCO (1-E)Et = (1-.5723)at INCO (l-B) Et = at 4 4 fl HUDSON BAY (1-.67ZB)(1—B )Et = (1-.8538 lat LOUISIANA (I-E)Et = .348 + (1-.363B4)at BAYUK (1-.519B+.47OBZ)Et = .259+at 4 AMERICAN SEATING (l-.403E)(I-E4)Et 3 (1-.8313433t INTERNATIONAL PAPER (l-B(l-B4)Et : (1—.83134)at GREAT NORTHERN cl-En:t = (1-.477E3)at UNION camp . (1-.309B4)(1-B)Et - (1-.44933)at + .428 WESTVACO (l-.8993)(1-B4)Et = (1-.7273‘).t ALLIED CHEMICAL (l‘.38634)(1-B)Et = (1-.5388)at DUPONT (l-.357B+.34OBZ)(l-B)Et - at 4 4 HERCULES (l-.4863)(1-B )Et = (1—.5313 )at UNION CARBIDE (1-.423B)(1‘B)Et = at CITIES SERVICE (1+.4SSBZIII-B)Et = (1-.407B)at PHILLIPS (1-B)Et = (l-.5038)at ROYAL DUTCH L1-.39832)(1“B)Et = (l-.3153-.48583)at VULCAN (1-b)(1-E4)E = a t t 4 4 INLAND STEEL (l-.5293)(1-B )Et 3 (1'.803B )at KAISER STEEL (l-B)Et = (l-.4558)at U. S. STEEL ALCOA REYNOLDS CATERPILLAR MAYTAG CHRYSLER FORD GENERAL MOTORS EATON ROLLINS 127 APPENDIX B (cont‘d) (1-.92034)a 4 (1-.7SlB) (1-B )Et 1:. (1- . 6868) (1-34) Et (1- . 78684) at (l-. 5128) (ll-84) (l-B) £1: = (1-. 50732) at (1-.45134)(1-E)Et (1-.so732)at (b.4913) (1‘34”. u-. 75134) a t (1- . 66634) a 4 (l-.5988).(1-B )Et t (1-.654R)(1-E4)Et (1-.94os4_)at (1- . 3598) (1-84) El: (71-. 85684) at (1- . 61234) at (l-.7BSB)(1-B4)Et 4 (l-B )Et 3 '396.,+at INOO HUDSON LOUISIANA LAND BAYUK 128 APPENDIX C T? MODELS 4 (1-8)CPt = (.985)(1-B)Et + (1-.4388 )at (1-8)CPt 8 (1.038+.06983)(1-8)Et + .577 + at (1-84)CF£ I .959(1-84)E + 1+.80383 a t 1-.5723 t (I-Emrt = (1519+.33132+I73536)(i-EIEt+at CFt ' (.519-.21283)Et+.461+° 1 a£ A‘ AMERICAN-SEATING (J.-'13a)c1=‘t .. 1.005(1-13’515t + .029 + at GREAT NORTHERN (I-Eui-E‘mrt = (I-En:t + 1-.3723 at 1-.4SSB4 "4 INTERNATIONAL PAPER‘l-B)(l-B4)CFt = .928(1-8’(1-84)Et + (1-.82884)at UNION '. CAMP WESTVAOO UNION’CARBIDE CITIES SERVICE PHILLIPS u-m'cr't - (.’59"I-.16713)41-13)}:t + a v(1-8)CFt 8 .865-h5588s (1-8)Et + 1-.4518 a (1--13)CPt = 1..05()(J.--B)1=:t + at (1-8)(l-84)CFt 3 (1.109-1.0598)(1-84)8t + 1.2938 at 1+.54sa4- (l-B)CFt - (.956.:.2308)(-8)Et + at (1-B)CFt - .980(1-8)Et + 1.341 + 1 4 at _ 41-.3743 4 4 4 (1-8 )crt - .596(1-B )Et + 1-.sssa at 1-.asoa (1-8)C1"t 8 .93911-8)Et+.913+ 1-.4448 at 1-.36184 g t 1-.5963‘ 4 2 t 1-.334B 1+.3898 129 APPENDIX C Cont'd ROYAL DUTCH manort a (1.226+.3853+.10332)(I-E)Et + ‘ 1 at 1+.43532 4 -- 4 4 VULCAN (1-8)(1-8 )crt = l.025(1-8)(1—B )Et + (1-.8878 )at 4 4 INLAND (1-3 )CFt = 1.003(1-3 )Et + 1 at 1-.44OE+.3323’4 KAISER (l-E)crt = (1.0SO)(1-8)Eti+ at 4 4 . 4 U.S. STEEL (1‘3 )CFt I 1.205(1-B )Et + 1‘.773B at - 1-.6718 . 4 ' 4 4 ALCOA . (l-B )crt = 1.068(1-8 )Et + 1-.ssaa at + 2.506 . ' ' - 4 1-.307B+.7708 REYNOLDS (1-8)(1-84)CFt = (-.216+.1478+.23582)(1-84)Et_1 + at CATERPILLAR 4 (l-B)CFt = 1.007(1—8)Et +.770 + at MAYTAG (1-34)crt - .967(1-B4)Et + (1-.67534)at 4 4 4 CHRYSLER (1-3 met a 1.042(1-3 )Et + 1.5595 (1-B)at 1+.27BE4 FORD (1-34)crt s .968(1-E4)E + 1 a + 9.402 1-.4618 (.950 -.24485)(1-84)Et + at i 4 GENERAL MOTORS (1-8 )CFt . ' 4 EATON (1-84)CFt = .885(1-B4)Et + (1-.6558 -.3278 )(1-8)at ' I 4 0 7’ + 18434)(1+B4)E + 1 a RDLLINS. (1-B ) = (1. 8 . t . t 1-.7018 Appendix D DEPRECIATION PERCENTAOES ASARco INC. INco LTD. HUDSON BAY HININe LOUISIANA LAND & EXP. BAYUK CICAR AMERICAN SEATING INTERNATIONAL PAPER eREAT NORTHERN NEKOOSA UNION CAMP CORP. UESTUACO CORP. ALLIED CHEHICAL CORP. DUPONT HERCULES INC. UNION CARBIDE INC. CITIES SERVICE CORP. 130 58.4% 32.4% 43.8% 36.0% 15.4% 31.2% 30.7% 36.9% 22.2% 28.6% 38.0% 38.9% .39.6% 32.7% 46.1% 131 Appendix D (cont’d.) PHILLIPS PETROLEUM co. 22.5% ROYAL DUTCH PETROLEUM co. 23.9% . VULCAN 30.5% INLAND STEEL CO. 35.3% KAISER STEEL CORP. 175.7% u. S. STEEL CORP. £51.2% ALCOA A 35.3% REYNOLDS METALS 26.7% CATERPILLAR TRACTOR CO.' I 20.4% MAYTAO co. . 3.5% CHRYSLER CORP. 56.4% FORD MOTOR co. , 35.0% ecNERAL MOTORS CORP. 31.4% EATON CORP. 13.3% ROLLINS 19.1% Appendix E TAIL AREAS OF THE CHI-SQUARE DISTRIBUTION DEGREES OF FREEDOM VALUES AT SIGNIFICANCE LEVELS .95 .19 .25 9 15.9 14.7 11.4 10 13.3 16.0 12.5 11 19.7 17.3 13.7 12 21.0 13.5 '14.3_ 132 Appendix F DIAGNOSTIC STATISTICS - UNIVARIATE CASH FLOW MODELS FIRM ASARCO INC. INCO LTD. HUDSON BAY MINING LOUISIANA LAND & EXP. BAYUK CIGAR AMERICAN SEATING INTERNATIONAL PAPER _GREAT NORTHERN NEKOOSA UNION CAMP CORP. NESTVACO CORP. ALLIED CHEMICAL CORP. DUPONT HERCULES INC. BOX-PIERCE STATISTIC 12.032 13.253 12.036 12.537 9.467 11.697 11.530 12.032 5.031 6.374 7.963 5.341 6.431 133 DF 12 1O 1O 1O 11 11 11 11 1O 1O PROD. RESIDUAL OCC.. ) .25 ) .25 ) .25 ) .25 MEAN SQUARE 43.49 .' 1 14. 92 11.22 3.23 .21 .12 59.68. 56.18 364.39 26.79 134 Appendix F (cont’d.) UNION CARBIDE INC. CITIES SERVICE CORP. PHILLIPS PETROLEUM CO. ROYAL DUTCH PETROLEUM CO. VULCAN INLAND STEEL CO. KAISER STEEL CORP. U. S. STEEL CORP. ALCOA REYNOLDS METALS CATERPILLAR TRACTOR CO. MAYTAG CO. CHRYSLER CORP. FORD MOTOR CO. GENERAL MOTORS CORP. EATON CORP. ROLLINS 11.891 6.599 9.811 9.357 6.507 16.414 14.939 7.954 15.374 11.464 10.397 3.624 7.580 7.965 9.682 9.997 4.687 11 10 10 11 11 10 11 10 10 10 10 10 10 10 10 10 11 .25 .25 .25 .25 .25 .09 .10 .25 .10 .25 .25 .25 .25 .25 .25 .25 .25 135.43 136.45 139.63 6518.20 1.09 76.98 26.07 1235.10 98.73 53.34 129.26 3.34 1823.60 5853.00 '42.070.00 9.28 .24 Appendix G DIAGNOSTIC STATISTICS - UNIVARIATE EARNINGS MODELS FIRM ASARCO INC. INCO LTD. HUDSON BAY MINING LOUISIANA LAND & EXP. DAYUK CIGAR AMERICAN SEATING INTERNATIONAL PAPER GREAT NORTHERN NEKOOSA UNION CAMP CORP. '. NESTVACO CORP, ALLIED CHEMICAL CORP. DUPONT 'HERCULES INC. BOX-PIERCE DF STATISTIC 13.434 12.926 11.941 5.087 13.529 9.611 17.404 13.583 4.097 8.523 5.832 8.408 4.127 135 12 10 10 10 11 11 10 10 10 10 PROD. RESIDUAL OCC. ) .25 ) .25 ) .25 > .25 ) .10 ) .25 > .10 > .25 ) .25 MEAN SQUARE 43.48 I" 1 06. 1° 3. 55 2.22 .02 .11 54.73 4.29 4.65 5.23 32.43 35.45 136 Appendix G (cont’d) UNION CARBIDE CORP. CITIES SERVICE CORP. PHILLIPS PETROLEUM CO. ROYAL DUTCH PETROLEUM CO. VULCAN INLAND STEEL 00.1 KAISER STEEL CORP. U. S. STEEL CORP. ALCOA‘ REYNOLDS METALS CATERPILLAR TRACTOR CO. __MAYTAC CO. CHRYSLER CORP. FORD MOTOR CO. GENERAL MOTORS CORP. EATON CORP. ROLLINS 15.910 13.244 7.802 5.684 4.651 7.551 17.235 10.739 8.722 4.362 9.929 3.695 8.110 9.737 9.949 11.095 6.486 11 10 11 12 10 11 10 10 10 10 10 10 10 10 10 11 ) .10 ) .25 ) .10 ) .25 ) .25 ). 25 ) .25 ) .25 ) .25 ) .25 129.61 68.77 160.16 4’ 263. 00 .87 62.27 25.59 755.67 64.26 121.99 123.02 3.55 11539.20 5556.40 ) .25 401045.00 ) .25 ) .25 9.869 .15 Appendix H DIAGNOSTIC STATISTICS - TRANSFER FUNCTION MODELS PIRM DOX-PIERCE‘ DF PROD. RESIDUAL STATISTIC OCC. MEAN SQUARE ASARCO INC. 10.732 11 ) .25 47.45 INCO LTD. 17.211 11 1 .10 2.23 HUDSON BAY MINING 13.737 10 > .10 12.53 LOUISIANA LAND AND EXP. 14.172 12 ) .25 2.33 BAYUK CICAR 15.500 ' 10 > .10 .01 AMERICAN SEATING 3.393 11 > .25 .01 INTERNATIONAL PAPER 12.959 11 > .25 11.36 GREAT NORTHERN NEKOOSA 9.371 10 > .25 1.34 UNION CAMP CORP. 15.601 11 > .10 .11 NESTVACO CORP. ‘12.495 10 1 .25 .53 ALLIED CHEMICAL CORP. 6.323 12 > .25. 13.30 DUPONT 7.623 10 > .25 20.04 HERCULES INC. 7.796 10 1 .25 13.02~ 137 138 Appendix H (cont’d.) 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