fII'II
6’26“”

III I II55II‘“‘.‘.I

‘IIIII ‘ III ‘55

'||‘:' I 'IrIufi. 6' 666666
I 5 ‘5'5. .555I‘55555I5I‘5
6 .-’ 53M 6 III 566666556666
II "““5 ‘5 ‘I 5‘5I ‘5‘5‘ ”Ila; 1515
III III—5555' 5555‘ III I" “II I" 5.
I " III“ I‘I‘I‘ I ‘I IIWIII‘I ‘In‘!
6.565. III}, ,5; “'5‘
IJ 666M III‘II‘ 61615 IIIII I 5

I‘fl‘ “wwwq 55‘ h‘ W.” ._ III".%"H'KLJfiuVI. ” .
5 II II '55 I“ 555 IIIII"“‘II :‘55555‘5‘ .-5

I6 .6555 I :6 “I55 I‘I‘IW 5-5555 III"

IIIIM

:.$51
3:25?- ..-£;.,.£_ .,.
-
“. 4“
=33" m3 525;?“
a,
-
......:..>.m:.

1':
2‘. Q!
6 ‘.o-. ‘ ‘-

— vlgv '. ”.2. .
“1-3:. .-'-"- ' 5
.".-.':-°~":__~'~x.-."

:: 2‘

_ -":?
4.21:: 5

WM... .....-...
u--
4- .

¢'- 1‘ o
4- .

-
n - .

I-

6» h Hm

'55_16I

   
   

   

5555555;-

x‘: I ' : o 'v :3 ' 'Z I. .
I I’ 9 6§IIIEEJ§6£ - : a, t ' '5' I : 5
T .m _.'¢ I if .. .
x ‘5 '5 ' I .J n? ‘.
I: h. I. U u

. .. .:

 

      
  

    
       

15$
-............- W
. .M
by.
5

  

    
 
 
       
 
 
  

5‘26“,

IIm5 ”6
55555

I, 6‘65 6655 III

6::I5 655I I‘IIII III!» 5‘6

fiflfij fi#‘ 6 “$5“ I

  

  

J 55' II‘I‘III III
II

     
   
     
   
  
     
    
 
 
  

 

  

 

 
  
  

.II‘ ‘ “ I‘III‘ III 55 ’5“ ‘.55I‘I5I5~“‘”~*5‘53'i5"
II III III ‘III “ E.E?5"-II‘IIII ‘I‘I‘I‘III‘I 6I5I5IIII5‘III5‘5 3“ “' II55 ;,-. '
‘5 55 III “III ”51.165555 5255' Iflsz' “”535
. :.I5555I 5'55555IIII" ' ~-
I .' -- vir
RI 56I3HIIII1“ IJIIIIIII‘ “"‘II In“ I‘I‘I’IIII‘I ‘
‘. "'I «I I
ISIIII‘HI ‘Isu066 MHI .3 ' "ir.‘
{5166 ‘III‘ 1,5‘5‘II,IIIII‘II 555IIII6II _ .1513? " f 565i .
I‘IIIIII'I5IITIIIIIIIIIIIIIIII‘II‘IIIIII‘IIIIEI‘II-v.F ‘5“ ‘MI‘IIEIEI
5.5655515 IIIIIIIIIIIIIIIIII 5II’5I5‘I5I... 55555I I5
1‘5 5 5 ‘ 5 555‘
II'h‘IIIIIIII III“ IIIIII'I I366 5'II‘5 II‘I‘IIHI‘III ‘s‘I, I

I. I 55555 II‘II‘I‘II‘ III I‘IIII‘56 II 5‘55
I I 6II‘66 dIIII? IIIIII‘ I‘I'IIIIIJ‘II‘I II IIIIIII‘J I :II“!
I; I? II‘ ' 5 ‘ 5'II III "“I‘ 55;

WEB-:5 'g‘ - '
III-III“? I'II _ I‘IjIIIe. IIIJIIII III

.
I.

I 5Q6I6,W‘&u mI
I‘II‘I ‘ III III“ 555 "I III" 5 - =I "
I'II‘I‘I IIIIIII.“ ,,,, 66‘ .‘ "‘IV‘III‘I '

‘I ‘II 2.5.: .,‘I. :

I '2; . I gpl‘f‘é‘lflifi “£16.? IIIII IIBIIIIiIITI‘II 6661 III}! :6 :65? 56.5.6 ,,
I A " III i. Y| ‘ 5 5
5 III-III III 5‘55“ I’I‘II‘ I5

 

M
.A:.x

  

 

 

THESlS g
I 2?. #1; I
it? ,‘ii '6' 3- Q3 ETV' y

q“ ’3' 33 w,

. 3" AIL'J' 5.1 V4113? i'i'iate
Unfiverséty

This is to certify that the

thesis entitled

A MULTIPLE FORECASTING SYSTEM FOR THE
TELECOMMUNICATION INDUSTRY

presented by

Charles M. Holmes

has been accepted towards fulfillment
of the requirements for

 

M.A. degree in Telecommunication

@l/Mw

Major professo{/

D Qty/CA 22] ”7ij RObert E. Yadon
ate '
U U /

 

 

 

0-7539 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

MSU

LIBRARIES
.—_—L

RETURNING MATERIALS:
Place in book drop to
remove this checkout from
your record. FINES will

 

 

 

be charged if book is
returned after the date
stamped below.

 

 

33-4

R04

 

‘5 ‘V L. 4| 1‘ 1‘ '4' ‘ ‘5 I}?!
3? LaL: a :t- :4:-

:2: USE Chili

I 41- A——'- FPO-4‘ (qr-nfl-V r- —-"-"'
6 . .1 L

 

 

A MULTIPLE FORECASTING SYSTEM FOR THE
TELECOMMUNICATION INDUSTRY

By

/7/—- 5759/

Charles M. Holmes

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF ARTS

Department of Telecommunication

1983

Accepted by the faculty of the Department of Telecommunication,
College of Communication Arts and Sciences, Michigan State University,

in partial fulfillment of the requirements for the Masters of Arts

@Mww

Director of The51s

degree.

Coo right by
CHA LES N. HOLMES
1983

ABSTRACT

A MULTIPLE FORECASTING SYSTEM FOR THE
TELECOMMUNICATION INDUSTRY

By

Charles w. Holmes

The purpose of this study is to develop a computerized multiple
forecasting system for use in the telecommunication industry. This
quantitative tool is designed for both managers and potential investors
who must prepare realistic projections of business activity.

Several different methods of time-series analysis are used in
the program, each having strengths and weaknesses in handling various
data sets. Any data set introduced into the system will follow a
pattern or trend. The individual forecasting routines attempt to
match the pattern and project it into the future. The forecasting
method which comes closest in matching the pattern will provide the
most accurate forecasts.

The system evaluates itself with built-in measures of accuracy
for each method including variance, standard error and the number of
residuals exceeding two standard deviations. The system then provides
a method analysis using the mean square error for each routine in order

to identify the method which provides the best set of forecasts.

ACKNOWLEDGEMENTS

This thesis would not have been completed without the
encouragement and guidance of Dr. Robert E. Yadon. I would like
to thank him for his support and most of all for his patience.

I must also thank Linda Yadon for her hospitality and inspiring
good nature. Without her graciousness, this task would certainly

have been unbearable.

TABLE OF CONTENTS

Page

LIST OF TABLES ........................ vi

LIST OF FIGURES ooooooooooooooooooooooo v1. .i
CHAPTER

I. INTRODUCTION AND STATEMENT OF PURPOSE ....... 1

Introduction ................... 1

Statement of Purpose ............... 3

Scope of Study ................... 5

NOTES ....................... 8

11. REVIEW OF LITERATURE ................ 10

Forecasting Simulation ............... 11

Telecommunication Acquisition Models ........ l4

NOTES ....................... 21

III. FORECASTING METHODOLOGY .............. 23

Introduction .................... 23

Forecasting Defined ,,,,,,,,,,,,,,,, 23

Forecasting Components ............... 24

Forecasting Methods ................ 27

NOTES ...................... 46

IV. THE MULTIPLE FORECASTING PROGRAM .......... 50

Introduction ................... 50

The Data Set ................... 51

Forecasting Routines ................ 52

iv

CHAPTER Page
IV. (continued)

The Program ..................... 58

Sample Run ...................... 6O

NOTES ........................ 74

V. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS ....... 75
Introduction ..................... 75

Summary of Results .................. 75
Limitations ..................... 77
Conclusions ..................... 79
Recommendations ................... 79
BIBLIOGRAPHY ............. , ............. 82
APPENDIX ............................ 84

Table

LIST OF TABLES

Page

Buffalo Viewership Trends ............... 4
Forecasting Possibilities ............... 11
Listing and Ranking of Radio Stations in Hypothetical

Market ...................... 17
Comparison Between Audience Shares and Theoretical

Shares ...................... 18
Monthly Revenues for a Midwest Radio Station . . . . 51
Control Cards and Data Deck ............. 58
Contrgl Card Specifications for the Sample Computer 60

un ........................

vi

Figure

3-1.
3-2.
3-3.
3-4.

LIST OF FIGURES

Page
Horizontal Data Pattern ............... 26
Seasonal Data Pattern ................ 26
Cyclical Data Pattern ................ 26
Trend Data Pattern .................. 26

vii

CHAPTER I

INTRODUCTION AND STATEMENT OF PURPOSE

Introduction

 

Broadcast station acquisition involves many steps; the most
critical entails the process of investment analysis. Because first
time investors are generally inexperienced in the businesses of
broadcasting, lack of specific skills and knowledge pertinent to the
industry can severely compound their investment risk.1 These potential
station owners suffer the most from the absence of a comprehensive
industry tool for evaluating purchase criteria.

Without proper financial insights, the neophyte buyer is at the
mercy of the seller who has at least three years broadcast experience.
In addition, the seller receives a differential advantage from media
brokers who get a commission based on the selling price.2

Successful buying, therefore, lies in the preparation of a sound
financial plan. Ideally, the plan will serve two purposes. First,
future benefits of the purchase can be determined; investors need to
assess both risk and earning potential when contemplating an
acquisition. Second, financial forecasts are part of the prospectus
used to obtain external capital. A thoughtfully prepared, concise

proposal often makes the difference between securing a loan or being

rejected.

While broadcasting has become a lucrative venture that doesn't
always require a great deal of starting capital, it is nevertheless,
a volatile and high-risk business. The complexity associated with
broadcast acqusition is emphasized by the National Association of
Broadcasters, who maintain that a broadcast station "is far from a
traditional franchise type business."5 Yet, the trade in radio stations,
the IJsual outlet for the first time investor, is steadily increasing.

In 1979, 546 commercial stations changed hands for an average

station price of $6l4,000. In l975, only 363 stations were sold for

an average price of $361,063.6 Although small station investors have
relied on banks and seller financing as a way of obtaining external
capital, the increase in station trade combined with the increase in
station price has strained the availability of traditional equity sources.

Financing options for broadcasters are further limited because of

two other supply factors.

l. Accelerating inflationary factors, coupled with heightened
uncertainty with respect to long-term funds markets have
reduced availability of fixed rate seller-note financing.

2. Accelerating cost of funds coupled with record loan losses
have substantially reduced regional bank availability of
fixed rate term loan packages.7

The odds of obtaining suitable financing are greatly increased

by having a complete, realistic, and professional presentation. Two
major factors are considered by a lender in determining the degree of
risk involved with a loan. First, a potential lender evaluates the
borrower's ability to generate cash flow for repayment of principal and

interest. Second, the potential lender appraises its own ability to

recover principal in the event of default. Lenders, therefore, are

primarily interested in operational results, both historical and
projected, especially cash flow, after debt service.8

Thorough financial planning entails the anticipation of as many
of the lender's objections as possible and resolving them in the
proposal before they are raised.9 The astute investor will spend
considerable time supporting the projections with realistic assumptions.
These accurate forecasts aare essential; a borrower has nothing to gain
by being overly conservative. At the same time, a borrower, by being

10
too optimistic, will endanger loan opportunities.

Statement of Purpose

 

This study attempts to develop and construct a forecasting tool
for broadcast investors who, on their own, may not be able to prepare
realistic projections of business activity.

Radio and television sales, for example, are influenced by supply
and demand factors which will cause revenues to fluctuate by seasonal
or cyclical trends.11 These trends occur, not only because of limited
inventory and seasonal demand, but also because of audience levels
which are rarely constant throughout the year. For example, in
Buffalo, New York the prime time TV viewing levels peak in February
and drop to their lowest level in July.12

Since the determining factor in station profitability is manage-
ment,13 forecasting becomes a necessary tool because of the increased
operational costs and the fact that the profit margin can be very

susceptible to "variations in an increasing sales pattern."14

Table 1. Buffalo Viewership Trends

 

Households Using Television (HUT)
July 1982 November 1982 February 1983 May 1983

 

Monday-Friday 43% 62% 66% 58%
8—11 p.m.

 

SOURCE: Nielsen Station Index, "Buffalo, New York," Viewers in
Profile, (Northbrook, IL, A.C. Nielsen Company, May
1983), p. 4.

Forecasting models must be able to provide management with realistic
projections in the fact of uncertainty. This is especially important,
and becomes complicated, because of the various trends associated with
the financial elements in broadcasting.

Therefore, determining a station's financial value and its earnings
ability forces an investor to rethink the basic soundness of an
acquisition while supplying valuable financial material for potential
lenders. Both prospective owners and financiers need a complete finan-
cial package used to make the requisite determination that a project
has merit.

As an ancillary use, students studying the art of broadcast
acquisition will have the opportunity to apply acquisition theories
normally covered in formal "lecture" type instruction. Although this

thesis will be geared to professionals, the student proficient in

elementary managerial finance will find the concepts and principles
easy to understand and follow.

The tool developed as part of this study, is a computer-based
financial planning forecasting model. The program will strive to
describe the dynamic behavior of a broadcast station in terms of its
future financial health. It can then be used to test financial
hypotheses about the property in question.

The power of simulation forecasting lies in its ability to predict
the behavior of a system without disturbing normal operations. Through
the use of forecasting, the prospective station owner is able to
prepare projections of property performance, The validity of such an
analysis is, of course, directly related to the accuracy of the fore-

casting model.

Scope of the Study

Although the basic financial principles used apply to all areas
of the telecommunication industry, this study will focus on, and use
as examples, only broadcast station properties. There are several
reasons for this: first, the greatest number of transactions occur
with radio.15

Second, the Federal Communication Commission's attempt to add
more radio stations to the spectrum, combined with the push for

low-power television, will create a greater supply of affordable

broadcast outlets.

There are also some inherent limitations associated with this
study. Due to the complex nature of broadcast acquisition, the
model cannot be all inclusive. A station's financial forecast does not
give an accurate indication of a market's (or station's) complete
potential. Investors must also prepare a comprehensive market analysis.
In some situations the market analysis should be prepared before the
station financial analysis.16

A potential investor must consider market variables such as:
total advertising dollars, total retail sales, consumer spendable
dollars, media competition and industrial stability. The inability
of the proposed study to accommodate a subjective station analysis is
another limitation of this study. The prospective owner must decide if
a format needs changing or if personnel should be replaced. Affiliation
and other contracts have to be evaluated along with the physical station
property. Major replacement costs may be incurred causing a disruption
in the financial plan.

Although no program can take the place of thorough acquisition
planning, this simulation model will alleviate some of the financial
uncertainties. It will help investors answer questions about a station's
earning potential and give them help in determining the proper structure
for financing.

Reviewing a station's present standing is only part of the invest-
ment analysis. Prudent investors need to develop long-range financial
plans and goals. Many troubles associated with financing and profit-
ability reflect poor and/or inappropriate preparation. The blame,

however, cannot lie solely with the investor inexperienced in station

acquisition. Without a tool for broadcast investment analysis, they

may not be able to avoid the financial pitfalls encountered when buying
17
a station.

CHAPTER I--NOTES

1
Ward L. Quaal and James A. Brown, Broadcast Management,

 

2nd ed. (New York: Hastings House Publishers, l976), p. 281.

2
Stephen J. Sansweet, "How to Buy Your Own Radio Station,"

The Green Pages (l978), pp. 54-55.

 

3
National Association of Broadcasters, Purchasing a Broadcast

 

Station: A Buyer's Guide (Washington: National Association of

 

Broadcasters, 1978), p. 12.

4
Kay D. Ingle, "Radio Entrepreneurs Fill the Airways," Venture

(l979), pp. 62-63.

5
National Association of Broadcasters, Purchasing a Broadcast

 

Station: A Buyer's Guide, (May 1978), p. 2.

 

6
Barry J. Dickstein, "'True' Station Value is Key Ingredient in

Broadcast Financing," roadcast Financial Journal 10 (March l98l),
p. 16.

7
Ibid.

8
National Association of Broadcasters, Purchasing a Broadcast

 

Station: A Buyer's Guide, (May l978), p. 12.

 

9
Lee Hague, "Acquisition Financing: An Overview Update,"

Broadcast Financial Journal, 8 (March 1979), p. 2l.

 

10
Ibid.

11
Robert E. Yadon, "Application of Forecasting Techniques to the

Telecommunication Industry," (Department of Telecommunication, College
of Communication Arts and Sciences, Michigan State University, East
Lansing, MI, 1980), p. 7.

12
Nielsen Station Index, "Buffalo, New York," Viewers in Profile,

 

(Northbrook, IL, A.C. Nielsen Company, May l983), p. 4.

13
Ward L. Quaal and James A. Brown, Broadcast Management, p. 293.

14
Ibid., p. 304.

l5
C. David Ungruhe, "A Comparative Analysis of the Communications

Media," Valuation Reporter (First Quarter, 1979).

16
National Association of Broadcasters, Purchasing a Broadcast

 

Station: A Bgyer's Guide, p. 36.

l7
Harold Poole, "What's Your Station Worth?" Broadcast Financial

 

Journal, 8 (March l979), pp. 10—12.

CHAPTER II

REVIEW OF LITERATURE

The massive amount of work done in corporate modeling concerns
the ongoing dynamics of the firm, not acquisition financing. It
should be noted that there is a long history of both simulation model-
ing in general and forecasting simulation in particular, especially
since the advent and widespread use of the digital computer.

An examination of corporate and financial models as well as articles
relating to telecommunication acquisition suggest that the application
of simulation technology to telecommunication investment analysis is
appropriate and desirable, yet often lacks a comprehensive method of
accurately projecting such items as revenues, which are an integral
part of acquisition financing.

This chapter begins with a review of various discussions relating
to the role and application of forecasting simulation in business.

The chapter concludes with a broader discussion of telecommunication
acquisition models which provide insight into the decision making
process involved in acquisition financing. After reviewing these
models it becomes evident that what they lack is a quantitative fore-
casting component which reflects the ongoing dynamics of various

financial elements.

10

11

ForecastinggSimulation

 

Makridakis and Wheelwright suggest that the major role of fore-
casting "is to aid in assessing various future alternatives and the
levels of risk and return that are associated with each of them, so
that managers can effectively address this dilemma."2 The authors
also stress that forecasting is not just a statistical technique,
but an integral part of sociology, politics, economics and psychology.

A simple framework has been proposed to categorize forecasting
possibilities to help managers develop guidelines and act as a reference

point for planning applications.3

Table 2. Forecasting Possibilities

 

 

Implicit Explicit

Estimating the sales of Using a monthly meeting of
Intuitive Product A for the coming senior management to develop

month in an intuitive, ad forecasts for Product A for

hoc manner. the next month.

Predicting the sales of Obtaining monthly forecasts
Formal Product A for the coming for each major product group

month using a statistical on a specified date for use

forecasting method. in production planning.

 

SOURCE: Spyros Makridakis and Steven C. Wheelwright, The Handbook of
Forecasting: A Manager's Guide (New York: John Wiley & Sons,
1982), p. 5.

 

 

"Intuitive" forecasting consists of internal processes to planners
with regard to subjective and judgemental estimating procedures.
"Formal" methods, on the other hand, may be slightly more accurate than

intuitive procedures. Formal methods can be written down and provide

12

similar results regardless of the user.

The "implicit" column refers to forecasts which are not part
of plans or decisions being made. This is true even for formal procedures
which would not be part of specific plans or actions. Conversely,
"explicit" forecasting methods attempt to clearly define the value of
the forecast and use it in the decision making process.4

Makridakis and Wheelwright emphasize that forecasting procedures
usually begin on the intuitive and implicit level then move toward
formal explicit techniques. This systematic approach often leads to
"significant improvement in forecasting performance" which allows decision
makers to better understand future uncertainties and evaluate the

5
associated levels of risk.

Forecastigg Procedures

 

A discussion of the selection of proper forecasting procedures is
provided by Fildes who proposes that forecasting choices are based on a
broad range of considerations:

1. Prior Beliefs of the Forecaster--The forecaster is likely

 

to be influenced by past experiences and related research with which
the forecaster feels comfortable.

2. How the Forecast is to be Used-~The methods employed will

 

be directed toward an expected goal.

3. Complexity and Comprehensiveness--When the model is too

 

complicated it probably won't be used because it won't be understood.
However, the model must include all pertinent elements or the forecast
will not accomplish required goals.

4. Cqmprehensive Testing--Several parallel models ought to be

 

13

6
developed and used to test the primary model's performance.

Fildes breaks down the methods of forecasting into three
broad classes:

The judgmental-~where individual Opinions are
processed, perhaps in a complicated fashion.

The extrapolative--where forecasts are made for
a particular variable using only that variable's
past history. The patterns identified in the
past are assumed to hold over to the future.

The causal (or structural)--where an attempt is
made to identify relationships between variables
that have held in the past, for example, volume
of brand sales and that product's relative price.
The relationships are then assumed to hold into
the future.7

Most techniques use more than just one of the above approaches,
while most models tend to include parts of all these methods.

More specifically, Hanke and Reitsch list four basic steps in
developing a forecasting procedure:
Data collection
Data reduction or condensation

Model building
Model extrapolation (the actual forecast)

#(JONH

Although these steps are geared to statistical methods of
forecasting, Hanke and Reitsch do not diminish the importance of
intuitive methods for predicting the future in an attempt to reduce risk
and uncertainty. They propose that quantitative techniques should
supplement the "gut" feelings, common sense, and management ability
of decision makers.

Forecasting, then, is useful if it reduces uncertainty while
resulting in informed decisions that have increased value over and

9
above the cost required to produce the forecast.

14

Sullivan and Claycombe sum up forecasting as:
"A blend of science and art that defies precise
definition for a successful application.
Preparation of a forecast entails more than just
using historical data and mathematical formulas
to project into the future. The key to realistic
forecasting is the inclusion of informed judgement
and intuition into the methodological framework
being employed in order to minimize uncertainty

associated with the future development, or event,
in question."

Telecommunication Acquisition Models

Chapman and Associates, a national media brokerage firm, currently
uses a computer program for broadcast station investment analysis.
The program is lauded by Chapman as a time saving device giving the
brokers and investors pertinent financial data along with projections
of financial activity.11

The program utilizes nine financial variables in the calculations.
They are: income, expense, profit or loss, loan principal payment,
loan interest payment, leverage factors, the depreciation schedule,
covenants not to compete, and the appreciation factor. The program
makes financial assumptions about each variable and takes into account
the variable's effect on each other. The naive financial assumptions
used are based on static percentages. For example, the fixed expenses
may be set to increase by six percent over a ten-year pro forma period,
while the sales figure automatically increases by nine percent.
This shows growth occurring in an exponential manner year to year when,

in fact, this growth should be linear. Month to month or quarter to

quarter variables, on the other hand, usually change exponentially.

15

The output from the program includes a pro forma profit and
loss statement, a ten-year cash flow analysis, a return on investment
analysis which incorporates an analysis of return on down payment,
return on total payments, and a return on purchase price. The broker or
analyst takes the outputs and evaluates them with the client to determine
if the results fall into line with the goals and needs of the investor.
There are several advantages to the Chapman model. The most
obvious is the freedom to utilize the buyer's preference for a certain
type of investment analysis. For example, the program can accommodate
the buyer who wants to consider the purchase “in terms of a multiple
of cash flow, a "time-gross" formula, or a return on investment analysis.
Like the "TEEM" model to be discussed, the Chapman program
relies on the insights and experience of the broker to evaluate the
results of the financial analysts. A significant problem with the
program is its reliance on a set percentage rate to estimate growth.
There is no allowance for seasonal trends or more cyclical variations
such as the quadrennial effect associated with the broadcast industry
(a jump in revenue every four years due to the national elections and
Olympics). The article does not discuss. the basis of the financial
assumptions. How were they derived? How reliable are they? How are the
changes and shifts in the marketplace evaluated? Additional methods,
like risk and ratio analysis are also missing from the Chapman program.
Another non-computerized method for valuing a station is used by
analyst David Schutz. Schutz emphasizes profitability as the key
factor in station valuation.12 The prices paid for a station, according

to Schutz reflect the future earnings that they will likely generate.

16

The difficulty for the buyer is in the determination of the future
earnings.

An extensive market analysis is used to aid in the determination
of station value. The variables which are part of the market analysis
include the total market advertising revenues, disposable income, total
retail sales, and advertising competition. The buyer is advised to
ascertain the vitality of the market which should reflect the potential
of the station in question.

The most interesting component of the Schutz analysis is the
subjective evaluation of the station and a comparison of theoretical
versus actual audience share. The variables used in this mathematical
evaluation of theoretical (or potential) share are based on such factors
as power, frequency, and hours of operation. Schutz uses a hypothetical
market to illustrate the method of obtaining the theoretical share
(Table 3).

A comparison can then be made between actual and theoretical shares
to see if the station is performing "better" or "worse" than technical
conditions suggest it "should" (Table 4). Schutz estimates that if a
station is within 20 percent of its theoretical share, it is considered
normal."14

This kind of analysis is beneficial to a potential owner who is
then able to look at a station with a poor actual share (compared to the
theoretical share) and determine if the problem is indicative of poor
management. Likewise a station might be doing better than it should
indicating that little can be done in the way of improvement.

This idea of earning potential and sound management is discussed

by Schutz in the close of the article.

17

. . .ew .a .Am~m_ »_=qv 6H
.ocagwmcwo:M\acmEmowcoz ammoumocm =.:wmocmm m xppmwm :owpmum wasp m~= .Npasom .m cw>ma "mumzom

 

.mcwcczoc on one pcmucwa ooH Page“ “on ou mmcmgm

.o.H m>_momc mesa; umumswpca sow: meowumum mp_;3 m. m>mmuoc meowamum mswuxmo

.o.H m>wmomc mcomumum z; .A~:¥ cm .cmcw ccwumpm\omofiv\ mwmmn wzp co apco mcowamum z< ou umw_nn<
.Lmasac m_o;z ummcmm: op umuczoc use Aooo.fl\cmzon :owumumyx mo mwmmn on» :o emuaasoum

.mmmmmpo m>wpumnmmc any we meowumom com zpmscoc=
uwcmcwmcoo mm: “L mocmm ucmsummcu mumcwnmm cm>wa coma we: we: “Lava; mccmucm mcowumum 2; mo mmmo on» cm

MQ'LD

 

 

 

H
mnmm mucaoa Peach
GAS .mqm. a,“ o.H N coo.m coo.m ~.mm m
wmfi 0.6 o.H o.~ N coo.m ooo.m m.¢m o
Nfim o.m o.H o.~ m ooo.- ooo.m~ n.mo~ u
§NH m.~ o.~ a. fi omm ooo.~ ommfi mug:
&om w.¢ o.H w. m ooo.~ ooo.o~ oomH m
xmfi m.~ m. m.H H -o- ooo.~ owe <
mgmsm mucwoa cowumcmqo Xucmscmcd cmzoa ugmwz xmo A~:z\~:¥v cowumum
m _muoh a mo mesa: m Amuumzv cmzom xocmaamcd

_

Boxes: Pmawuaeuoasz cw meowpmpm owuam Lo esteem“ gem accomws .m 6_nac
mH

18

Table 4. Comparison Between Audience Shares and Theoretical Shares

 

 

2
Net Weekly 1 Audience Theoretical
Circulation Share Share
A 31,300 13% 12%
B 60,100 25% 20%
WDES 26,500 11% 12%
D 45,700 19% 21%
E 38,400 16% 17%
F 38,500 16% 17%
Total 240,500 100%

 

1
In place of Net Weekly Circulation, Average Quarter Hour Audience
(6:00 a.m.-midnight, Mon.-Sun.) could be used.

2
From Table 3.

SOURCE: David E. Schutz, "Is That Station Really a Bargain," Broadcast
Management/Engineering, 14 (July 1978), p. 84.

 

19

Your success as a station owner will not be determined

solely by your ability to acquire a station at a low

price. Instead it will be determined by your ability

to run your station efficiently and effectively.15

The final telecommunication acquisition model considered here
was developed by Wagner, Akutagawa, and Cuneo (1969). The Telecommunica-
tions Earning Estimation Model (TEEM) was designed for the Security
Analysts of Wells Fargo Bank. TEEM is a probabilistic model used to
derive an earnings estimate for a company by means of simulation. The
model was built to assist an operating analyst in simulating the expected
financial behavior of one company at a time, one year at a time.16

The operating income statement and the funds flow statement
provide the framework over which TEEM operates. The analyst, not the
model, is responsible for the accuracy of the financial estimates used
in the calculations. The analyst has the option of accepting a system-
generated estimate of earnings, or the analyst can replace it with one
he or she has generated. In other words, the estimates used in the model
are only advisory to the analyst.

The output of the program includes standard financial statements
with a built-in probability distribution expressed as "Pessimistic,"
"Most Likely," and "Optimistic." The range is arbitrarily set at two
standard deviations from the "Most Likely" parameter.

TEEM is not applicable to this Taaper because it cannot be used
as a training tool for inexperienced investors. It relies too heavily
on the implicit knowledge of a seasoned analyst who makes similar
investment decisions as part of everyday business. What TEEM did

was to speed-up the process of investment analysis. The program did not

give the analyst any new information and was weak in the sense that the

20

analyst had the option of overriding most variable assumptions. These
shortcomings were so prevalent, that the authors considered TEEM some-
what of a failure. Although it was introduced to over 100 analysts,
no one elected to use it.'7

To investigate the reasons for its failure, the authors studied
the reliability of the model. Their study showed that the model did

not outperform the estimates of the analysts, the very people it was

designed to help.

21

CHAPTER II--NOTES

1
Robert C . Meier, William T. Newell, and Harold L. Pazer,

Simulation in Business and Economics (Englewood Cliffs, New Jersey:
Prentice Hall, Inc., 1969), p. 1.

2
Spyros Makridakis and Steven C. Wheelwright, The Handbook

 

of Forecasting: A Manager's Guide (New York: John Wiley & Sons,
1982), p. 7.

3
Ibid., p. 5

4
Ibid.

5
Ibid.

6
Robert Fildes, "Forecasting: The Issues," The Handbook of

 

Forecasting: A Manager's Guide, ed. Spyros Makridakis and Steven C.
Wheelwright (New York: John Wiley & Sons, 1982), pp. 89-90.

7
Ibid., p. 92.

8
John E. Hanke and Arthur G. Reitsch, Business Forecasting

 

(Boston, MA: Allyn and Bacon, Inc., 1981), p. 4.

9
William G. Sullivan and W. Wayne Claycombe, Fundamentals of

 

Forecasting (Reston, VA: Reston Publishing Company, Inc., 1977), p. 2.

 

10
Ibid., PP. 1-2.

22

11
Chapman & Associates, "Using a Computer for Investment Analysis,"

Broadcast Financial Journal 7 (January 1978).

 

12
David E. Schutz, "Is That Station Really a Bargain?," Broadcast

Management/Engineering, 14 (July 1978), p. 82.

 

13
Ibid., p. 87.

14
David E. Schutz, "Is That Station Really a Bargain?, Part II."

Broadcast Management/Engineering 14 (August 1978), p. 86.

 

15
Ibid., p. 38.

16
Albert N. Schrieber, ed., Corporate Simulation Models(Seattle, WA:

 

University of Washington, 1970), pp. 396—399.

17
Ibid., p. 416.

CHAPTER III

FORECASTING METHODOLOGY

Introduction

 

Successful buying of telecommunication properties, as stated
in Chapter 1, lies in the preparation of a sound financial plan.
The plan will determine possible future benefits of the purchase
and secondly, financial forecasts are used in the prospectus required
by lending institutions.

This chapter will explore methods of financial forecasting which,
when used by potential investors, should provide projections of earning
ability. These predictions of future events can be obtained by

discovering patterns of events in the past.1

Forecasting Defined

 

Having the ability to make decisions based on information which
predicts uncontrollable business events should give management an
improved choice of options while attempting to reduce risk. Fore-
casting is the prediction of future events with the intent of reducing
the risk involved in decision making. While usually wrong, the infor-
mation from the forecasting process is used to improve the decision

making process.2

23

24

There are basically two types Of forecasting. The first involves
"qualitative" estimations Of future events. This subjective method
relies on the Opinions Of experts who use various tools such as
marketing tests, customer surveys, sales force estimates and historical
data. Decisions are based on "Opinions."3

The second basic type Of forecasting revolves around "quantitative"
methods which use procedures that explicitly define how the forecast
is determined. The Operations are mathematical in nature with the logic
clearly stated. Quantitative forecasting examines historical data
to determine the underlying process generating the values Of each variable
and, assuming this process follows some stable pattern, using the
information to extrapolate the process into the future.4

Although business decisions must be based on both qualitative
and quantitative information, this study is the formulation Of an
analytical tool for potential investors through the use Of a computer

which relies on quantitative data. Therefore, only statistical fore-

casting procedures will be explored.

Forecasting Components

 

Patterns

Operational variables such as revenues and expenses change
over time and follow some sort Of pattern. All forecasting methods
assume that a pattern or relationship exists which can be uncovered,
identified and used as the basis for preparing a forecast. An

effective forecasting procedure depends on matching a pattern with

25

a particular technique that can handle and project that pattern into
the future.5

There are four common patterns that are considered the most
important. These patterns can be found alone or in combination.
The first basic pattern is "horizontal" or "stationary" in nature and
does not increase or decrease in any systematic way (Figure 3-1). The
average mean value Of the data remains constant. On the other hand,
a "seasonal" pattern exists where a series Of values fluctuate according
to some seasonal factor or factors (Figure 3-2). Lawn mower sales is
an example of a seasonal series. A "cyclical" pattern is very similar
to a seasonal pattern but the length Of the cycle is generally longer
than one year (Figure 3-3). This particular type Of fluctuation is
Often the most difficult to predict because it doesn't repeat itself
at constant invervals Of time. Finally, when there is a general increase
or decrease in a value over time, the fluctuation follows a "trend"

6
pattern (Figure 3-4).

Time Elements

 

Forecasting patterns involve the mapping Of some variable over
time. When used in forecasting, the variable time consists Of three
separate elements. The first is the basic unit Of time for which the
forecasts are made called the forecast "period." The period can be a
week, month, quarter, year, or whatever length of time makes sense to
the problem at hand. The forecasting "horizon" is the length of time
(or "lead-time") in the future for which the forecast is made. The
forecast could be done for a year broken down by months. In this

case, the period is a month and the horizon is a year. Finally,

26

:cmuuma name came» .vum mczmwd

as.

k
2.: ___1«

 

assasooosznONo-o
.H — q _ H fl _ W

 

 

ccmupma mama FmOPFOxu .m-m wcamwd

«Err A1

033.2.
3880“.

 

ccwuuma mama _mcomwmm .~-m mgamwd

«B. :2 22 $2
seamsmmmiummzumm
8.:q____q______q__q

 

 

.325,
80980...
cgmppma mums FouconLo: .Flm mczawd
0:... h A
:32
0335 >
3380 m

 

27

the period over which each new forecast is prepared, is called the
forecast "interval." The forecast interval is Often the same as the
period which means the forecast is revised each period using the most
current data point to update the forecast.7

When the forecast is revised each period and the horizon or lead-
time remains constant, the forecast is Operating on a "moving horizon"
basis. For example, if the problem involves forecasting monthly sales
for the next year on a continual basis, the period and interval would
be a month and the moving horizon would be a year. SO as each month's
data is received, the lead-time is moved ahead by 12 months. The fore-
cast usually becomes less accurate when the forecast lead-time is
increased. In other words, the shorter the lead-time, the quicker

8
the forecast model can react to error.

Forecasting Methods

 

Forecasting systems use both quantitative and qualitative methods
Of analysis. The statistical methods lend Objectivity to the system
and quantify historical trends. Forecasts done by statistical methods

become another piece Of information used by financial managers prior to
9
making decisions.

Montgomery and Johnson list eight factors which contribute
to the selection Of appropriate forecasting methods:

Form of forecast required.

Forecast horizon, period, and interval.

Data availability.

Accuracy required.

Behavior Of process being forecast (demand pattern).
Cost Of development, installation, and operation.

ONU‘I-DwN-d

28

7. Ease Of operation. 10
8. Management comprehension and cooperation.

Since this study concentrates on the quantitative methods Of forecasting,
qualitative considerations will not be discussed. First, a brief
description Of general forecasting models will be presented followed

by a discussion of several common interactive forecasting methods which
range from the basic regression methods through the more complex
exponential smoothing methods including Winters' Method which takes

into account seasonal trends.

Forecasting Models

 

There are two basic models used in forecasting: "time-series"
and "causal" models. Very simply, a time-series is a time ordered
sequence Of Observations Of a variable. A time-series analysis uses
values Of a variable over time in order to develop a model for pre-
dicting the future such as revenues over months Of a year.11

Causal models examine the relationship Of the primary variable
and other time-series. An example Of a causal model would be the
correlation Of revenues with share of audience. There are two
limitations to the use Of causal models. First, the independent variable,
in this case share Of audience, must be known at the time Of forecasting
revenues. Since the share Of audience cannot be explicitly known
in advance, the entire projection for revenue is tainted. The second.
drawback to the use Of causal models involves the complex nature Of

12
the forecast in terms of the amount Of computation and data handling.

Therefore, this study will concentrate on the various methods Of time-

series analysis that have a direct application to broadcasting.

29

Regression

 

Simple regression utilizes the "line of best fit" by plotting
the dependent variable, say revenues, over the independent variable
time and drawing a straight line through the middle Of the data
points.13 The Object Of regression is to arrive at an equation
for the line through the data which minimizes the squared differences
between the line and the actual data.14 In this method the key
variable (revenue) is directly dependent upon the independent variable
(time). Simply put, the variable revenues increases or decreases

at the same rate every period.

15
The equation for simple regression is:
Y = A + B * Y (1)
Where: A--is the "Y intercept" which is the value

Of the line when X = O.

B--is the regression coefficient and indicates
how much the value Of Y changes when the
value Of X changes one unit. B is also

called the "slope" of the line.

Y--is the dependent variable for which the

equation is being solved.

X-—is the independent variable (time).

30

A and B are the "parameters" Of the equation and must be solved
for by using the method Of least squares in such a way that the sum Of

squared errors is minimized. In other words, the deviations above

 

 

the "line" will exactly Offset the deviations below the "line."16
B = N*2XY - X*2Y ( )
2
N*2X2 - (2X)2
A = ZY - B*£X
'_N_ N (3)
Where: N--is the number Of data points.

The most Obvious disadvantage to the use Of regression analysis
in forecasting is the fact that not all data points fall on the
regression line and the data points may take the form Of a cyclical or
seasonal pattern which is not accounted for by using linear regression

methods.17

Another disadvantage to the use Of regression forecasts
is that the forecast cannot be updated when new data points become
available. If new estimates for the parmeters are needed, an entire

new set Of data points must be used.18

Simple Moving Averages

 

In general, moving average techniques attempt to eliminate
randomness in a time-series. The goal is to distinguish between the
random fluctuations and the basic underlying pattern in the historical
data. This Objective is achieved by averaging ("smoothing") the
historical values in order to eliminate the extreme values in the

sequence. The forecast is then based on the smoothed value.19

31

The technique Of "simple (or single) moving averages" takes a
set Of historical values, finding their average and then using that
average as the forecast for the upcoming period. The number of data
points used in the averaging procedure (N) is determined by the Operator

20 Since the key variable tO be forecast can change

and remains constant.
slowly over time, it would make sense that the more recent Observations
in the historical trend should hold more weight than observations in
the distant past. ‘Because Of this, only the most current data points
might be used allowing the model tO react to data shifts. This is

where the "moving" concept comes into play. As each new data point

becomes available, the Oldest is discarded.

 

The formula for an N-period simple moving average is:21
St = Xt-l I Xt-Z 1 °°' 1 Xt-N
N (4)
Where: St—-is the forecast for period t.
Xt--is the actual value at period t.

N--is the number Of values used in the average.

Since the formula averages only the last N values, if N is
increased the model is less sensitive to variations and takes longer to
adjust to data shifts. Conversely, a small N reacts quickly to change
but may force the model tO react to random variations which are not part

Of the underlying data pattern.22

32

Double Moving Averages

 

For data with a linear or quadratic trend the single moving
average procedure would produce misleading forecasts because the
projection would "lag" behind the data shifts. TO correct for this

23 The double moving average

lag; a; "double moving average" is used.
is simply the average of the single moving average. The double moving
average treats the single moving average as a single data point.

The formula for an N-period double moving average is:24

. III III III
Mt|2l Mt + Mt_1 + ... + Mt N (5)

 

N

Note: The [2| refers to double moving average,
not the squared value. Likewise the III
is the single moving average.

The forecast equation is then:

Yt+x = At + Bt*X (This is the regression equation)
' (6)

1 2
_ ZMtl I - Mtl I (7)

>
I

Where:

B ='(_N'E_1—)*(Mt'l' ' Mt'z') (8)

The primary advantage Of moving average techniques over regression
is that the forecast can be quickly revised with a smaller number Of
calculations as each new data point is received“ Secondly, this
procedure allows the forecaster to place more weight on current data
rather than treating all data with equal importance. This also minimizes
data storage since only the most recent N values are used in the

averaging.25

33

There are, however, disadvantages to moving average forecasting
procedures. These have to do with the basic premise Of the techniques,
which assumes that the trends and patterns will continue into the future.
An erratic data point which breaks the norm could be the start Of a new
shift in the data or it could be a "freak" value that would throw the
entire forecast Off balance.

Another limitation to moving averages is that the technique gives
equal weight to each of the last N Observations. NO weight is given
to the discarded values. While it is preferable to weight the current
values more heavily, it may not be advantageous tO completely disregard

past Observations.26

The next section addresses this problem by
describing techniques which focus attention on recent values without

ignoring past data points.

Single Exponential Smoothing

 

Developed within the past 25 years, exponential smoothing
techniques have become popular due tO their simplicity, computational
efficiency, reasonable accurateness, and the fact that they require only

a few data points to produce forecasts.27

Like averaging techniques,
smoothing procedures can be used for simple linear trends with more
random or seasonal trends.

"Single exponential smoothing" is based on averaging (smoothing)
past data points in a decreasing (exponential) manner.28 The new estimate
is Obtained by modifying the Old estimate by some fraction Of the fore-

cast error which results from the previous estimate. In other words,

the error between the actual and the forecasted value for the current

34

period is used for correcting the forecast for the upcoming period.
The fraction used in the correction is generally denoted by the Greek
letter Alpha (a), called the "smoothing constant."

The general formula for single exponential smoothing is:29

S = OXt + (l-O)S

t+1 t

Where: St--is the exponentially smoothed value in period t.
a--is the smoothing contant.

Xt--is the actual value at period t.

If the equation for St is expanded by substituting the equation

for St’ the equation then becomes:

S

OX + (l-O) (OX

t+1 t (10)

1 + (l-O) S

t- t-l)

)2

OX 'tO(1-O) Xt-l + (l-O S

t t-l

When the new equation includes the formula for St-l the above

equation becomes:

2 x + 6(1-6)3 xt_ +

S = (xx + (1-0.) X 3

t+1 t + O(1-O)

t-l t-Z

and so on ... (11)

The above equation shows that decreasing weights are given to Older

Observations. Another form Of the equation is:

S = S + O X -S (12)

t+1 t ( t t)

This formula is simply the Old forecast St plus 6 times the error

(Xt - S Montgomery and Johnson refer to this equation in their

t)°

35

definition Of moving averages which is: "a procedure that adjusts
the smoothed statistic by an amount that is proportional tO the most

recent forecast error."3O

Double Exponential Smoothing

 

In the same way that the single moving average technique showed
signs Of "lag," the single exponential smoothing model also lags behind

31 The double exponential

the true value when forecasting a linear trend.
smoothing model is completely analogous to double moving averages in that
we can add to the single exponential smoothing value the difference

between this value and the double exponential smoothing value and then

adjust for the trend:32
A) s (1): x +(1-)s|1| (13)
t a t “ t-l
lg) [1| 121
B) St = OSt + (l-O) St-l (14)

Like double moving averages, the forecast for double exponential

smoothing is:

st+x = At + Bt x (15)
At = zsill- 512' (16)
B: = 'fi3;‘ (s11:ll - 512') (17)

Note: |2| refers to second order exponential
smoothing, not the squared value.

36

Where: a--is the smoothing constant.

X--is the number Of periods ahead to be forecasted.

Double exponential smoothing can handle a trend pattern better
than single exponential smoothing because it reacts more quickly to the
shift in the data values. The forecast follows the trend more closely

and eliminates the problems with lag.

Triple Exponential Smoothing

If the underlying pattern Of the data is curved rather than
linear, the double exponential smoothing technique becomes inadequate.33
Exponential smoothing can be expanded to estimate coefficients in
polynomials Of any degree. Triple exponential smoothing techniques carry

the general formulas into the next higher polynomial. The formula for

 

 

triple exponential smoothing and the resulting forecast are:34
131. l2! I3]
St - OSt + (l-a) St-l (18)
v = A + B x = c x2 (19)
t+X t t t
- Ill I21 I31
At — 35t - 3st + st (20)
B = 01‘ ((6-56)S 1' l - 2 (5-4,)5 '2 1+ (4-3,)sl3l) (21)
t 2 t t t
2(l-O)
2
ct = a (st)1| - 2542' + 543' ) (22)
(1-a12

Note: I2] and |3| refer to the second and third order
exponential smoothing not squared or cubed values.

37

As mentioned, the exponential smoothing procedures are Often
more desirable than moving averages because they only require a few
data points to generate a forecast while the moving averages require
the storage and handling Of N data points. Secondly, the exponential
smoothing models do not "discard" Older values, they just give less
weight to Observations in the past.

Before moving to more advanced forecasting models, two concepts
should be addressed which are integral parts Of exponential smoothing
procedures. They are model initialization and the choice Of an

appropriate smoothing constant.

Model Initialization

 

Initial values are needed for all types Of exponential smoothing.
The number and type Of initial values depends on the type Of smoothing
employed. The need for initialization arises only when smoothing is
used for the first time. Even then, the problem is more theoretical
than real.35

The reason for initialization can be seen by examining the

smoothing formula:

St+1 = OXt + (fl-(1)51; (23)

Where: Xt--is the most recent value.
St--is the latest forecast.

St+1--is the forecast for the next period.

38

When T = 1:
$2 = 6X1 + (l-a)S1
In order to solve for 52, S1 must be known. The value Of S1
should have been S1 = 6X0 + (1-6)SO. It can be seen that XO does not
exist and SO cannot be found. In other words, 51 must be supplied in
order to solve for $2. The problem arises in that 51 cannot be found
in the data.36

Makridakis and Wheelwright suggest three approaches to arrive
at initialized values, assuming past data exists. First, the fore-
caster could separate the data into two parts using the first to
estimate the initial values and the second to estimate and check optimal
parameter values. A second approach involves the technique of back
forecasting. This approach inverts the data and starts the estimating
procedure from the most recent value and ending with the Oldest value.
What this does is provide parameter values and/or forecasts for the
beginning Of the data. These are then used as the initialized values
when the data is forecast in a normal (beginning to end) sequence.

Finally, the least squares method can be used. For instance,
in single exponential smoothing, 51 can be found by averaging the past
N observations. For linear forms Of exponential smoothing, A1 and B1
can be found by using the straight line equation to Obtain Al (the
intercept) and B1 (the slope) and using these as the starting parameter
values.37

When there are no past values, the forecaster can either wait

for data points or arbitrarily specify the initial values based on

39

common sense. Another arbitrary way Of assigning a value to S1 is to

make it equal to X1 and then start the forecasting.38

Choice Of a Smoothing Constant

 

The selection Of the appropriate smoothing constant along with
the choice Of the proper smoothing technique are the two most critical
decisions made by the forecaster. These decisions will determine whether
the forecasting process is a success or failure. The smoothing constant
(a) is critical because it is the control factor in determining the
number Of past Observations that influence the forecast. Small values
result in a slow response to data shifts because significant weight is
given tO many past Observations. Conversely, the larger constant gives
weight only to the most recent values which causes the system to react
more rapidly to shifts in the data.39

A rule Of thumb is to have the constant fall between 0.01 and

0.30.40

In general, if the underlying data pattern seems to remain fairly
constant, a small a should be used. Likewise, frequent and dramatic
shifts in the data ought tO be handled by using a larger smoothing
constant so the model can react quickly to the changes. This, however,

is precisely why the forecaster should proceed with caution in choosing
the constant. A tOO small valuefbr'the smoothing constant prevents

the model from responding quickly to a shift in the underlying pattern.
Yet, a constant that reacts very quickly could respond to a random
Observation which is not indicative Of the basic pattern.41

Although there is really nO explicit rule for arriving at an

apprOpriate constant, several approaches can aid the forecaster in

40

making an educated choice. One such approach is to arrive at a
smoothing constant which will give similar results found in moving

averages. The formula is:42

O= 2
N+l

Where: N--is the same number Of data points used in moving
averages.
Another technique would be to go through several iterations
using different constants in the exponential smoothing formula and
making a measure of effectiveness such as minimum sum Of squared errors.
Alternatively, if there are 36 data points available, a forecast could
be done using a particular constant on the first 24 Observations and

comparing the results tO the actual values in periods 25 through 36.

Winters' Method Of Exponential Smoothing

 

Many data sets, such as beer sales, broadcast revenues, or toy
sales can exhibit seasonal influences in addition to linear trends. The
previously mentioned exponential smoothing procedures control for
randomness and adjust for trends but they do not take into account
seasonality. Winters' Method is similar to double or triple exponential
smoothing but includeserladditional parameter which adjusts for seasonal
shifts in the data.43

There are four basic equations needed to arrive at a forecast

using Winters' Method:44

 

41

1. Estimate the current intercept:

X

A,c = 6(Ft_ ) + (1-6) (At-1+ Bt-l)
t-n

2. Estimate the lepe:

Bt = em, - Am) + u-s) 3H (25)
3. Solve for the updated seasonal factor:

X
_ t

Ft - 6(AZ) + (l—o) Ft-N (26)
4. Forecast for T periods ahead:

Yt+T = (At + BtT) F (27)

Where:

Xt-—is the observation at period t.

At--is the estimate Of the intercept Of the trend
line at t.

Bt--is the estimate Of the slope Of the trend line
at t.

N -- is the number Of Observations comprising
periodicity Of the data.

Ft--is the estimate of the multiplicative seasonal
factor at period t.

Ft_N--is the estimate Of the seasonal factor N
periods in the past.

F -- is used to denote the best estimate Of the
seasonal factor in period t+T.

6,6,o--are the smoothing constants.

42

The values for the smoothing constants in Winters' Method are
arrived at in the same general manner as a was in exponential smoothing.
However, with three constants, which can be used in many different
combinations, the task Of arriving at Optimum values is far more
difficult. The iterative process Of forming different combinations of
a, 8 and 0 would be computationally exhausting and near impossible tO dO
without the aid Of an Optimizing routine in a computer forecasting model.
Without such an aid the forecaster is forced to arbitrarily assign values

that lie between 0.01 and 0.30 as was done in exponential smoothing.

Box-Jenkins

 

There are other forecasting models beside the ones previously
mentioned which are useful in particular situations. One such method
is the Box-Jenkins approach tO time-series analysis which is a powerful
tool for providing accurate short-range forecasts. The methods and
formulas which are part Of the Box-Jenkins procedure are far tOO complicated
to be included in this study. More importantly this method, which combines
the strengths of autoregressive models with moving average techniques,
has several drawbacks.

First, a large amount Of data is required to complete the computa-
tions. For instance, at least 72 data points are needed tO forecast
seasonal data in a 12-month horizon. The model works best with many
Observations over a short period such as daily stock prices. Secondly,
there is nO easy way tO update the model with new data, which is
a strength Of smoothing methods. The model must be completely refitted
with the new data in order to update the forecast. This makes the cost

Of Operating the model prohibitive. Finally, the methodology is more

43

difficult to understand and the results are more difficult to comprehend

than in other methods.45

Evaluation of Forecasts

 

Referring back to the basic definition Of forecasting, one finds
the ideas Of uncertainty and randomness prevalent throughout the
discussion. Because this uncertainty exists in an uncontrollable
situation, randomness will always be present. Forecasting attempts
to minimize the uncertainty by minimizing the difference between the
forecasted value and the actual value.46

This difference, called "forecast error" should not, however, be
considered a negative aspect Of the forecasting situation. It should be
considered a given and used for its advantages. Because Of the wide
range Of forecasting procedures, performance evaluation is essential.
Forecast error is used to measure this performance.47

The first step in model evaluation is to define error, which is
simply the difference between the actual value and the predicted value.
This error is then statistically manipulated to provide different
measures Of reliability. One of the most basic is the measure Of error

dispersion around the mean, called the "standard deviation" and the

squared value called "variance." The formula for standard deviation

48
(Y-Y )2
s =\/———————2 R (28)

N --1

is:

 

44

Where: Y--is the actual value.
YR--is the forecasted value.

N--is the number Of conservations.

If there are several residuals which differ greatly from the
mean (usually two standard deviations), the forecasting procedure can
be considered suspect in closely following the trends.49

Another measure Of error is to take the absolute value Of the
error value and compute the average (mean) error. This technique
is called the "mean absolute deviation" (MAD). A similar alternative
is to compute the "mean square error" (MSE). The MSE is Obtained by
squaring each error and finding the mean Of the squared values.

An advantage to using the MSE criterion is its ability to
penalize the forecast more for large deviations than small ones. For
instance, an error Of 2.00 is squared and then counts for four times
as much error as an error Of 1.00. By attempting tO minimize the mean
square error in the forecasting routine, it is assumed that several small
errors are more desirable than a few large deviations.50

When several different forecasting techniques are used simultaneously,
the Operator must know which procedure handles the data most efficiently.

By computing the mean square error for each technique, the Operator can
then choose forecasts generated by the procedure which produces the
smaller MSE. In this way a multiple forecasting technique can be
developed which analyzes different types Of data sets. The Operator
then has several techniques ready to use for any data set and does not

have tO redesign the entire forecasting system to fit particular

variables. In this way the MSE is not just used tO judge how

 

45

well a forecasting procedure works, but it also allows evaluation

between forecasting techniques.

46

CHAPTER III--NOTES

1Spyros Makridakis and Steven Wheelwright, Interactive Forecasting

(San Francisco: Holden-Day, Inc., 1978), p. 13.

2Douglas Montgomery and LynwOOd Johnson, Forecasting and Time

Series Analysis (New York: McGraw-Hill, Inc., 1976), p. 2.

 

31bid., p. 7.

4Ibid.

5Steven C. Wheelwright and Spyros Makridakis, Forecasting Methods

for Management (New York: John Wiley 8 Sons, 1973), p. 19.

 

61bid., pp. 19-21.

7Montgomery and Johnson, Forecasting and Time Series Analysis,

 

 

p. 4.

8Ibid., p. 5.

91bid., p. 8.

loIbid., p. 9.

111bid., p. 7.

121bid., p. 8.

13Makridakis and Wheelwright, Interactive Forecasting, p. 120.
14

William G. Sullivan and W. Wayne Claycombe, Fundamentals Of

 

Forecasting (Reston, VA: Reston Publishing Company, Inc., 1977), p. 60.

 

lslbid.

47

16Wheelwright and Makridakis, Forecasting Methods for Management,

p. 107.

17Ibid., p. 137.

18Makridakis and Wheelwright, Interactive ForeCasting, p. 121.

 

19Wheelwright and Makridakis, Forecasting Methods for Management,

p. 55.

201616.

211616.

221bid., p. 88.

23Sullivan and Claycombe, Fundamentals Of Forecasting, p. 88.

 

24Ibid.

251bid., p. 83.

26Wheelwright and Makridakis, Forecastipg Methods for Management,

 

p. 62.

27Makridakis and Wheelwright, Interactive Forecasting, p. 58.

 

28Ibid.

29Wheelwright and Makridakis, Forecasting Methods for Management,

 

p. 62.

30Montgomery and Johnson, Forecasting and Time Series Analysis,

p. 49.

31Ibid., p. 57.

32Wheelwright and Makridakis, Forecasting Methods for Management,

pp. 71-72.

48

33Sullivan and Claycombe, Fundamentals of Forecasting, p. 95.

34Ibid., pp. 95—96.

 

35Wheelwright and Makridakis, Forecasting Methods for Management,
p. 80.

36Ibid., p. 79.

37Ibid.

38Ibid.

39

Spyros Makridakis and Steven C. Wheelwright, The Handbook Of

 

Forecasting: A Manager's Guide (New York: John Wiley & Sons, 1982),

 

 

 

 

p. 122.

40Montgomery and Johnson, Forecasting and Time Series Analysis,
p. 67.

411616.

42Sullivan and Claycombe, Fundamentals of Forecasting, p. 93.

43Wheelwright and Makridakis, Forecasting Methods for Management,
p. 73.

44Sullivan and Claycombe, Fundamentals Of ForeCasting, pp. 101-102.

 

45John E. Hanke and Arthur G. Reitsch, Business Forecasting

(Boston, MA: Allyn and Bacon, Inc., 1981), pp. 306-307.

46Wheelwright and Makridakis, Forecasting Methods for Management,

 

p. 22.

49

47Makridakis and Wheelwright, The Handbook of Forecasting:

 

A Manager's Guide, p. 457.

48Hanke and Reitsch, Business Forecasting, p. 7.

 

49Wheelwright and Makridakis, Forecasting Methods for Management,

 

p. 112.

501bid., p. 23.

CHAPTER IV

THE MULTIPLE FORECASTING PROGRAM

Introduction

 

This chapter presents a computer program developed to generate
multiple forecasts using the following methods Of time-series analysis:
1. Simple Regression
Single Moving Average
Double Moving Average
Single Exponential Smoothing
Double Exponential Smoothing

Triple Exponential Smoothing

\IO‘U'IDOON

Winters' Method

In addition, the program provides checks Of accuracy using
calculations Of variance, standard error and the number Of residuals
exceeding two standard deviations. The program also provides a
"method analysis" based on the comparison Of mean square error (MSE)
generated for each forecasting routine. This method analysis indicates
which of the above methods provides the "best" forecast for a particular
data set.

A data set and manually generated forecasts will be used to
validate the methods employed. A computer program using and evaluating

the forecasting methods is then introduced which will expand and

50

51

expedite the manual calculations. Finally, resultsobtained by using
the computer program with the data set are presented at the end of the

chapter.

The Data Set

 

In order tO test the application Of time-series techniques to
broadcast properties, monthly revenue figures from a Midwest radio
station, in a medium-sized market are used. The station is in a
market that contains at least five other commercial radio stations which
compete for available advertising revenue. Thus, the value Of a program

such as this, to forecast future revenues is apparent.

Table 5. Monthly Revenues for a Midwest Radio Station.

 

 

Month Period Revenue Month Period Revenue

January 1 $106,794 July 19 $139,617
February 2 116,734 August 20 153,507
March 3 126,114 September 21 148,409
April 4 113,021 October 22 183,845
May 5 119,626 November 23 171,785
June 6 117,485 December 24 176,756
July 7 119,626 January 25 127,109
August 8 112,130 February 26 130,440
September 9 111,678 March 27 140,694
October 10 139,704 April 28 159,302
November 11 135,321 May 29 162,168
December 12 152,337 June 30 158,753
January 13 86,111 July 31 152,182
February 14 105,933 August 32 168,858
March 15 116,682 September 33 157,313
April 16 129,772 October 34 207,745
May 17 157,178 November 35 194,117
June 18 148,367 December 36 180,291

 

52

Forecasting Routines

 

A sample forecast is manually generated from the data set for
each method in order tO validate the forecasting equations used in
the computer program. Each method uses the variables "X" to denote
the period and "Y" for the observation. The number Of periods used in
moving averages (N) has been set at 6. The exponential smoothing

constant (a) has been set at 0.15.

Simple Regression

 

1. Calculate the slope (B):

£(X*Y) - (X*ZY)

2X2 = (X*zx)

 

2,024.99

2. Calculate the intercept (A):

A = Y - (B*X)

104,976.61

3. Generate the forecast for 12 periods ahead (period 48):

YEST A + B * X

104,976.61 + 2,024.99 * 48

$202,175.52

53

Single Moving Average

 

1. Generate the forecast for the last period (36) and any
future period.

zY (30 to 35)

SMA (36) = N

 

1,038,968
6

$173,161.33

Double Moving Average

 

1. Calculate the double moving average using the last N single
moving averages (periods 31 to 36):

2. Calculate the intercept (A) at period 36:

A(I)
A(36)

(SMA(I)*2) = DMA(I)

(173,161.33 * 2) - 159,125.69

187,136.97

3. Calculate the slope (B) at period 36:

(SMA(I) - DMA(I))*2

B(I) =

 

(173,161.33 - 159,125.69)*2

B(36) = 5

 

5,614.16

54

4. Generate the forecast for 12 periods ahead:

FDMA

A(36) + B(36) * 12

187,136.97 + 5,614.26 * 12

$254,508.09

Single Exponential Smoothing

 

l. Initialize the model using the first Observation:

SES(I) Y(1)

106,794

2. Generate subsequent forecasts using a:

SES(I) a*(Y(I) - SES(I-1))+ SES(I-I)

SES(2)

.15 * (116,734 - 106,794) + 106,794

$108,285

Double Exponential Smoothing

 

1. Initialize the model using the first Observation:

DES(I)

Y(1)

106,794
2. Generate subsequent forecasts using a:
DES(I) = ( a * SES(I)) + ((1 - a) * DES(I-1))

DES(36)

(.15 * 168,949.54) + (.85 * 151,598.34)

154,201.02

55

3. Calculate the intercept at period 36:

A(I) = (2 * SES(I)) = DES(I)

A(36) (2 * 168,949.54) - 154,201.02

183,698.06

4. Calculate the slope at period 36:
= (SES(I) - DES(I)) * a

(l-oT)

B(I)

 

(168,949.54 - 154,202.02) * .15

B(36) = .85

 

2,602.68
5. Generate the forecast for 12 periods ahead:

FDES

A(I) + B(I) * X

183,698.06 + 2,602,68 * 12

$214,930.22

Triple Exponential Smoothing

 

1. Initialize the model using the first Observation:

TES(1)

Y(1)

106,794
2. Generate subsequent TES values using a:

TES(I)

(O * DES(I)) + ((1 - a) * TES(I-I))

TES(36) (.15 * 154,201.02) + (.85 * 141,424.62)

14,334.08

3.

4.

5.

6.

56

Calculate the intercept (A) at period 36:
A(I) = (3 * SES(I)) - ( 3 * DES(I)) + TES(I-I)

A(36)

(3 * 168,949.54) - (3 * 154,201.02) + 141,424.62

185,670.18

Calculate the slope (B) at period 36:

B(I) =( °'
2 * (1 - a

* ((6 - 5 * a) * SES(I)) -

 

)2)

((10 — 8 * O) * DES(I)) + ((4 - 3 * O) * TES (I))

B(36) .1 * (886,982.25 - 1,356,968.98 + 508,860.84)

3,887.70

Calculate the third polynomial coefficient at period 36:

2

C(1) = (1 f a ) * (353(1) - ( 2 * DES(I)) + TES(1))

 

C(36)

.03 * (168,949.54 - 2 * 154,201.02 + 143,341.08)

116.66
Generate the forecast for 12 periods ahead:

C
2 * X

FTES(I)

A(I) + B(I) * X + (

 

2 )

FTES(36) 185,670.18 + (3,887.70 * 12) + .40

$232,322.98

57

Winters' Method

 

In this example, the equations needed tO solve for each
component of the Winters' equation are listed in Chapter III. The

basic forecast for 12 periods ahead is:

FFP(I) (A + B * X) * S

FFP(36) (169,993.58 + 1,592.20 * 12) * 1.16

$219,355

Method Analysis

 

The above methods Of time-series analysis produce unique forecasts
for any given data set. A manager must choose the forecast generated
by the procedure that handles the data set most efficiently. TO measure
this "efficiency,” the "mean square error" (MSE) is computed for each
method:

1

=___*
MSE N 2E

2 (29)

Where: N--is the number Of residuals.

2E2--is the sum Of squared residuals.

The forecasting routine generating the smallest MSE is considered
the "best" method for a particular data set. This measure Of accuracy
lets management use several forecasting methods simultaneously and then
decide which method provides the most accurate forecasts Of future

activity.

58

The Program

 

Written in Fortran IV, the program is listed in its entirety in
the Appendix. The concept Of a multiple forecasting program is
derived from two sources. Sullivan and Claycombe designed a system
which fundamentally combined various forecasting methods into a single
program.1 Montgomery and Johnson developed a routine to find the
Optimum smoothing constants for use in Winters' Method Of exponential
smoothing.2 Neither program contained extensive checks Of accuracy
such as variance, standard deviation or number Of residuals exceeding
two standard deviations. In addition, neither program included a
comparative analysis based on each method's mean square error. Thus,

this program is an extension Of and improvement on other programs

commercially available.

Control Cards and Data Deck

 

Aside from the data set, several control cards must be input
by the user. The control card and data deck set-up are listed in

Table 6.

Table 6. Control Cards and Data Deck

 

 

Card Variable Name Format Description
1 N I3 Number Of data points.
X, Y 12, F8.0 Period and corresponding data.
NUM 13 Number Of data points used

for moving averages. NUM
must be an even multiple Of N.

Table 6. (continued)

59

 

 

Card Variable Name Format Description
ALPHA F5.3 Exponential smoothing constant.
T 12 Number Of periods ahead that

6 NW, N1, KS, KN,
LN, LT

7 (If KS = 0)
WALPHA, WBETA,

WGAMMA

7 (If KS =1)
AL, AD, AU,
BL, 30, BU,
GL, GD, DU

8 (If KN = 0)

9 (If KN = 0) BO
10 (If KN = 0) 5(1)
through
(L + 5)

2I3, 211, 213

3F4.0

9F4.0

the forecasts will be made.

These variables are all used in
Winters' Method:

NW--is the number Of data points
and must equal N.

N1--is the length Of the time
series used in model calcu-
lations.

KS--is set at 0 if the smoothing
constants are specified;
or set at 1 if smoothing
constant optimization is
desired.

KN--is set at 0 if initial values
are specified; or set at 1
if the initial values are to
be developed from the data.

LW--is the length Of season.
LT--is the forecast lead time.
Specified smoothing constants.

Lower limit, step size, and

upper limit Of smoothing
constants for the Optimization
routine. The upper limit must
be set one step size higher than
the desired upper limit.

Specified value Of permanent
component.

Specified value Of the trend
component.

Initial seasonal factors for
each Of L periods.

NOTE: Cards 8 through (L + 5) are needed only when KN = 0 (initial

values specified)

 

60

Sample Run

 

Using the data set listed in Table 5 and the control card

specifications listed below in Table 7 (as formatted in Table 6),

a sample computer run was made using the facilities Of the Michigan

State University Computer Center.

on pages 61-73.

Table 7.

The results (output) are included

Control Card Specifications for the Sample Computer Run

 

Card Variable

User Specification

Notes

 

l N

2-37 X, Y

38 NUM

39 ALPHA

40 T

41 NW
N1
KS
KN
LW
LT

42 AL, AD, AU
BL, BD, BU
GL, GD, GU

036

(See data set listed

006

0.15
12

36

24

For 36 periods Of data.
in Table 5)

6 months Of data used for
averaging.

Forecasts will be generated
for the next 12 months.

Length Of time series (36
periods).

24 months will be used in
model calculations.

Requesting Optimization of the
smoothing constants.

Initial values will be dev-
eloped from the data.

Length Of 1 season is 12
months.

The lead time is set at 1
period.

The lower limit for smoothing
constant Optimization is set
at 0.05 for each constant, the
steps will increase at rate Of
0.05 and the upper limit will
stop the Optimizing routine

at 0.30.

61

,.
'S
..

SERI

MULTIPLE FORECASTING OF A TIME

tOOSIMPLC REGRESSIONOfi.

ERROR ERROR-SO

FORECAST

579980Q56965539535581635910601909036
248702599164189351531537303167807275
cocooooooooooooooooooooooooooooooooo
90199955893531356972.0409388312550783
9590.2688401830043967860266983529R651
0015040235152306643058673389470Q1003
3461:..8502664“5153039305.“..03471871.409;,
0.47 722099138052070n_2699208356.nw.1733
98 21287517145801.7487325136360890.68

05b 3 .fiz9fiitfue7ingh..I976339fi1552 OKEDS
52 2 8306345451016 703135 94 053
2 1.2 5073 3

105873 2 213
1 1

2

00192336656633219001123366‘.“ ~33219°O
6““5“‘QSS~..55.:5‘55555554‘QRQ~000566
I......OOCOOOOOOOOOOOCOO0.00.0000...
77n¢r00806379r003906000-783926?0339888—3“
0065257027669960741~30137D..8R..737(P181561
270. . 81y.354fl0013667§.efl.9321419359‘.9.92‘
- 75 Q 9108357877638 “0387821165. 0382
1 o “.1. Zflqccl . 1. . 322444-1- - . 1... «mo-D1.

3.099577665443321100o.n.8776654¢3321100
6bSSSSSSSSS—DSSSSSSSQQQOQQQQQQQOQQQQQ
oooooooooooooooooooooooooooooooooooo
1.51.61.615161615151516161.61.6161.31. 5161.6
025702570257025702570257025702570257
0.135.11112222103334499555....666677779898
7911.570.135.191357911.57913579135791357
fi31111122222333334QR4455550666557???
1119.11.11.11111111111111111.1111¢A11111

000000000000000000000000000000000000
00000000000000000000000000000000E000
oonocoo-00000000000009oooooooooooooo
‘0.016560841.7132287779556904283253571
9312AL821~7BJOL1513877610n.4F.50“O.fiL6.3851419
77109461671.1.1.96711.654877106317151.712
56639792195255697991.93167009282970740
0.1211111133590125.3.3487723056556509?
111.111.111.111 11111111111111111111211

16:50.56?89011920456789? 32305678901234.56
111.1.1111.11226‘?.222222333331 ..J

5127804.00 SUM OF ERRORS: .00

SUM OF FORECASTS

11208116385.86

AVERAGE Y

SUM OF ERROR SOUARED=

= 192439.00

18.50

A OF SIMPLE REGPESSION

AVERAGE X:

2024.99

8 OF SIMPLE REGRESSION

109976.61

17487.07

STANDARD OEVIATION

365797677.01
NUMBER OF RESIDUALS EXCEEDING THO STANDARD DEVIATIONS

VARIANCE

1

SIMPLE REGRCSSION FORECASTS

FORECAST

PERIOD

90. R 77 6554933
33331.33331.33
0000000000..
1516151o31£.16
025702:..70.257
9.9990 0.1.. 011.11.
913580246502
788889999950
111111.1«11.12fis

780 . .....134:.L.Tr.
1.1.1.440 RQAARR

62

.00MCVIHG eVEPAGEScoc

SI“PLE MOVING AVERAGE

RESIDUAL RESIDUAL SO

FORECAST

ACTUAL

PERIOD

11111041154034806996494399315069158
. - a c g . 0912.00.703‘63.69060012036127
00000000..00000000000000.0000.
95200350839369}. 9.396950215196206
083671256500950.400859082910418.
086—366046511955374793226495361
996772b607735501.39215593052992
820638408760628499058106020063
675698926296660553973642371368
840810376..E112371C797674733 25.3
.973BaPfiLsrt.Qh¢‘.27$.3801a2833 09‘.
529.7?— 352‘ 023282 1 3 36
1 1 1 1 2

11111107370707.3707377377377770077307
......063656013601811316816165011356
.....OOOOOOOOO00.00.000.000...
772999575028925317056731180209
00752754 b9590850‘.5199954762882
963025391C166557 6127 6113723921
9.664592657635977695954195.“ 767
. . 212flcfl. 3212 311duafld. 1 1 Q2

.1I79$31071§:£JO71{X§J73t§193379i250011£r03
. c . . n . 06335301330919: 6935155135009 .053
0.000.000.0000oooooooooooooooo
R7C411. ......U? 1.58743138950441102261
715495.084 5363?.345 513:5 1118: 6.. .6
680606488606098115323104459781
(585026212144206572065196CE973
111122222222234455665554455567
111111111111111111111111111111

DD0000030000000000000000000000000000
r.0000000000000.000.900000000000000.00.10
coo-0.000.000.0000.-000.00.000.00...
QQ41656084167133.2287779.356909283283571
931228a3702313877 b1.-.0485049065851a19
77109461673310.6713654377146317183712
6561.97921952656975935316700923297740
0.12111111335801254354.677234565565098
111111111111 1111111111111111111211

12.545678901933056780.01234 567890.123956
1111 .1.J1s11.12222aAaco‘aczz‘.33333‘..

= 228320.00

OF RESIDUALS

SUM

4199410.00
14616452799.06

FORECASTS
SUM OF RESIDUAL SOUARED=

OF

SUM

21734.65

OF RESIDUALS EXCEEDING THO STANDARD DEVIATIONS=

STANDARD 0EVIATION=
FORECAST FOR ANY PERIOD AHEAD IS

472395047.55

VARIANCE=
NUHPER

1

173161.33

63

DCUPLE MOVIES AVERAGE

M(P) FORECAST RESIDUAL RESIDUAL-SO

ACTUAL

PERIOD

IQ¢IT.IIYJIIIv.va579676310000u42752933r47‘fie

. o n . c o u . - — . .34713:.6314Q62632637912357
OOOOOOOOOOOOOOOOOOOOOOOO
gecgeezdrdessn‘Qf“92315638“:
nspUg4515011357Ac1682775782
803nm.3R.527238Q982Q6Q‘280~2
8‘5309OQOR62378105358‘72
807790628-98912999‘695090
3376137‘859SRC98737RQ6979
63CQ1597337129177‘513Q57
Tagalog-329.710.21.222 16316672
11 2917 6 £58 1210 85
11 1 22 1 1

11111111111133.362723831319599182“.76

- . o . . o o u . u . .27F93173$929Q37260802572
oooooooooooooooooooooooo
7.221.88Q2560‘3881‘18‘9‘52
‘11‘86‘5269 0196931307899
ISB‘rtmb.‘8752.226152689192
23885c373Q-33108206117335
A3 . 3312 2 .552 1.113 42.
. c . . .

1117.7.111111133148387270.310.8219286636
. . . . . - . . . . . .2790.68263078Q37739197.22
coco-cocoooooooooooooooo
89..3992.39Q3282031333013
54939 01728796236130.453627
2437931662R137353Q553515
99512765496559?612879Rr45
23222122956878.65544.34678
11111111111.1111111111111

IIIYAIIIIIIIOAV81‘9~1272°’82‘2866839999
. c c - a u a . - - o6121960350,676A¢7‘°.7809.03636
.........................
Solarl‘uCJ‘lt.31.!‘835‘886‘77315
‘3‘043 USO—Dncgfioqlvl b109flu~90¢866n¢
E£~29.1o‘59.556211737170.5311
8C113332‘71754593577531.1259
126‘3‘22222233"555555‘.555‘.
1111111111111111111111111

nZUDnXUCnKEJOnZUOnXUOnIUOnXUDfiXUOnXQOOZEUOnXEUO
n52U0nX20052U0rzzbOnBEUODBKUCDEXEUOnKECOnfiEUO
o0.0000000000000000‘OOOOOOI....000...
44Q16553841713228777955b904283283571
9312292370.23138776100485049065951419
77199A61673319671365A877146317183712
6653979219525569799383167009289.8774”.
n.1211111133580125635487723A5655655G 8
1;141¢q.1¢1.....1.1¢1¢1; 1;1¢1;1¢1‘1;1;1;141¢1;1‘1.1;1A1‘1;1¢1;q;nch14

19.1.4567895 1951u“56789n Eln‘SR—uu6789fl-.123~56
1c .1111.1111229.2n¢n¢flt6 .fisz-J‘vasizxvis

74060.33

OF RESIDUALS

SUM

= 3592869o67
16853618988010

SUM OF FORECASTS

SUM OF RESIDUAL SQUARED

VARIANCE

28119.03

STANDARD DEVIATION

79C£79955o17

0

NUMBER OF RESIDUALS EICEEDING THO STANDARD DEVIATIONS

DOUBLE MOVING AVERAGE FORECASTS

FORECAST

PERIODS AHEAD

39.Q9=.15273R.4
247925702570

000000.00...
159389.515939.
123558912356
BROEZBRITBQZD
28.95062735‘
9900122334Q5
11222222222?

1.21.Q.:.L7 9 011,12
1Q.94

64

fi**EXPONENTIAL SHOOTHING*‘*

SHOOTHINB

SINGLE EXPONENTIAL

FORECAST RESIDUAL RESIDUAL-SO

E

ACTUAL

PERIOD

11002:.85850297259§.529533‘137515.16311
. . 0970389268.9926469665611931551180327
.0OOOOOIOOOOOOOOOOOOOO0.0.0.0000...
01.089901‘5215‘2431536352817293309783
CROITO’293227997C92520363R93£R725273
69.465531.43{.9n.331576.5599292323699128
33.0». “675.2r417‘54314cug75909486nu27376292
«51553539254675036299613274231.951253
8829195061682238‘549696989909‘62960
8744‘9R§.1~l325 068831305R813§1a¢cOO61e
91 79.3 8131.7 65.325213360021259 21727

3 63051 IRS-55238863 22 3 801

11. 1. 2 21

1100509259011067898035230139210473519
. .0°69710597R62320815565729601Q12§9Q8
ooo.coco-coco.ooooooooooooooooooaoo
0917-7136783ng1817690525‘Q6989P0632
42651225005930663329027978298717364
98059312181q2K~61635818O5566n¢8v¢907€93
9728.52267293 . 28313‘R8947QQ59183313

. .2133“. 132.121.4222”.- 11 1 531.

u .

7.10050 1859099967 212075810139890637591
. . UG:5280512.§5237919QO3‘329598687‘051
coo...coco-00.000000000000000.no...
Q599 703R6236260959C9QQ3RR8590292838
9P:.660539180781037EDQSEOITTEEG3Q054
72925329551011107059KST927C3£8162¥3119
680123Q33705977999.93527185469003426
n.01111111122111122233RQ5QR444555566
1111111111111111111111111111111111...

0005018590990672120758701398906375914
3D935390.512:7......37919993.32969968749515
ooooooooooooooooooooooooooooooooooooo
445987Q346236260959D9Q93R485942928389
99856:.05391507810378C45801776633AC5§4
7729253295KS110111072957927036816851199
65991239337C5977948935271859 69 90.342325
D09111111112211.1122233A9544Q4Q5555666
111111111111.1111111111.111111111111111

00000000000000COOCCDODOCDOCDOOCCUODOD
00080090000000CDOCDOOODDCOCODDOODDDOU
coo...goo-000.09.000.00.oooooooono...
0904165608A17132287779556934293283571.
93122923702313?7761004850A9065851419
77109ASIA-7331967136548771A6317183712
5563979219526569789383167009282877Q0
01211111133580125A35487721.9565565098
111111111111. 11111111111111111111211

‘33:,15456799 011053 ‘5 5789C1.23Q56189n.9 oars-3‘56
111111.1111222204222223333333

A1Q370026

RESIDUALS=

SUM OF

460663907Q

SUM OF FORECASTS:

17277075784o62

SUM OF RESIDUAL SOUARED

19429.50

STANDARD DEVIATION=

211311349.25
or RESIDUALS cxcscoruc THO STANDARD ozvxatxows

FORECAST FOR ANY PERIOD

VARIANCE:
NUHPER

3

1689A905Q

AHEAD IS

DOUBLE EXPONENTIAL SHOOTHING

RESIDUAL'SO

RESIDUAL

FORECAST

‘
U

ACTUAL DES

PLPIOD

65

HHOO OC‘NHHONOONNNOOOQFHOCNQnU‘QOOFFNU‘F
I A coOutta!-ChlthflC-mfinfina‘c‘OflOO‘FNONCJOEQO
OOOOOOOOOOOOOOOOOOOO0.000.000.0000.
acmmcmcuocomnawcmnwhcmmeAQNFknhcwt
tarmac-omho-«uoc0mmmn~a.~mnonor~ma.nonm\nh~osnw
~0rana¢1cwucmo¢~mncunm oceaamm~~v~ct~ucv~~0h¢¢
nochccrma‘mooflnmoasa‘cnhmmnmocncnnconnh
ummm-osnncownnomwnwnmo DCOQO‘FA ~‘DONC9OH
.na‘mwnnnmwmuwo‘hnnomcmofiumnoo ”HIHOON
duo"). nhtnc-o—OHMJO‘FINV‘IQ. omhnnaonnm Mn JNNN
0MB N Cn¢n¢:fl@ men ‘0 WHO‘ONOIOC ODnOON
N urn-ammo: "000‘ H NF! “ON
N v-a d No. N

an:rmacawncunnwmmonohathOcomN@omwwna
IIuorhcmommmmoncahmchwmoumnmhcunmwhoo
OOOOOOOOOIOOOOOOOOOO0.......0000...
oachmmnchomfikctnhhmunonhdo¢nouuonan
cnmmomma smock-ampmnmmnmmoncnommohwcnn
wnummomomcannmcmoxennwomomnh ¢mohnh
anon: noumnncohnunm Nounoaunwocho FGHDOOC
«I llN-«lenlunn a nu. Thu-c I Ito-cl
I II

HHOOU‘U‘00‘Dnamhdflsflflchv”NCQNOCOu-Oflh-CDKMDOWO
I luuomncmo‘hthawnnunmm cmwnawmaur «~0an
oooooooooooooooo00000000000000.0000
toammonmocmmooncomcI-ncNeo-onmc'mnoona‘n
whowr-mnawnmwnwo—cmmnfisoar-camnmmcmnona
FF ooops»;cmmwwwumohoconownc‘nnwuunor-o
\DU‘QOQFWFOIOC0n®GHNmO~JQHFNNONfl€DOOthfl
wouunua—oumwnwdumnntCcouhoflmflmmmoohw
mnudnnuuundddnn«dud—HaunuudnunHM—Q

uommeocmmnmnmcowomonncnommnonoocanon
IOwwmcSnumnhmwonwocunomcnmucwmfimnmfihc
000000.00....OOOOOOOOOOOOOOOOOQOOOO.
rumuwcoommwuwhmoommhommcmmhmnmomoww
NocmhdmNOGC“thwhmwnmmxmnthnmmnCHO
(“munghufithdh-JCJHONU‘U a,7~!~m~~c—ow:c~cnnr~m
an nronuHNNnCJHHuHHo-a—OHNNN

Hanocnmmmdwmucoamnncnuwhwuomocunammowmochuo
Icnnmnuocwuuomcooomunmmnnmnohnmcuomooo
coo-0.000000000000000...too.00.00000
0N0 aw home-«memnwnmncmcmmhmbomcov~t~ha
annoy-uncroommnntnr-mummmwommumoonnb‘nnmm
hmnmnumuomoowcuomucuscuhmma‘utm—mmocwo
mmOtun-Nbowhcflmmn—oha-¢0m000r)oc'~mr~~ummn
uonunnnanmwnwnawnnnccmwowmmmmw mocha":
MfiHflHHHv-io-oflMHHfiflddfidHNflflHHde-‘dflfifldfl

onan-«awocomwmcmnwhhnonmm—our-wmmnmmoonow
on 00' nN—ommocu-oto«mucuhhmmr-Nachdnnnmmcnno
00.000.00.00oooooooooooOooooooooooooo
CCFQFU‘NwUIOmvltw‘DfiHOOO-‘flCOONCDIOOI'INNFMHCGO‘EH
00~Om~¢oowmcGomochccmutmcfinwnomcficmmo
FFUL-‘fitNP—dnn or-m—ouwhnomthumnn ..IOCNNIDQU‘IN
\D\DFP'QJLUACJOVAKJPHDIDIDWVDFD‘C «ct-unmhnomnwnmomac
unoc-ouoanddn«unnundwmwwnnnnnnt0?!ttnn
HHNflfiMHocfldHHfiWHHNHNHnO-fiNHNHHv-QHHHHHH'Ofl

")uc ”)rumn floor; nonoooovzao "OLnoOOO-Jca-‘Jogoooo
O963000000C‘OOOOC‘OOC’DOOOOOODDOOOOOOOOOO
O0.000000000000000...0.00.00.00.00...
ccctnwnwowtflh—o'flfiflwhhbU‘anO‘ocNmnwmnnho-o
a-ndrgr.‘ [H “GP-l . ‘Jnfin¢.7~h \DF‘QCJ 31-2170 C‘.’~3VDU"LWHCNO‘
hh—onmcm—nwh dm-«mms—cnu‘nfloarhhdconn‘s—omnh—ON
QO'OMO-hmmdwDOJQWOU‘FFSO‘WGJIOHQFOCO‘NWNQOF-FCU
oraanHdn—nvcnnnmov-cwncnnncor-h(ancmomnomamw
duo-odowrcnvnu-u-cfi HHuHrcnnrnHHnHHMo-oudnnfiNHv-O

;‘ '0! .V'CWOFI‘U‘C‘ nmncmwhmmc fiNDCWQFflJO‘L‘rfl‘JnCIOO
HHH‘4rOr-0HHHHNC‘JOH'IN(¢t.\uCuanP)nF)F3nn

: 115679-69

SUI OF RESIDUALS

= Q935335o31
13133939022093

SUM OF FORECASTS

SUM OF RESIDUAL SOUARED=

VARIANCE:

20908.69

STANDARD DEVIATION

A165145Q0002

3

NUMBER OF RESIDUALS EXCEEDING THO STANDARD DEVIATIONS=

DOUBLE EXPONENTTAL SHOOTHING FORECASTS

FORECAST

PERIODS AHEAD

cmnmmrnuot-mn
hcuhonmmdumw
00.0.0000...
nnmm—ocmmwtho
OOOOfidv-OHNCJCJIO
no .n—osntmnnr-nth

dHflHv-‘HNNNCJNN

«Nl'ydmwh-ma-l o-ON
H'AH

TRIPLE EXPONENTIAL SHODTHING

FORECAST RESIDUAL RESIDUAL-SO

TC

TES TA

ACTUAL

PERIOD

66

HnouhflonfimemQU‘kWNv-dmthfimflFCNU‘CGMU‘NQO
I I owonhnm cmxmnmunamwm«fiddmnwonmhumcwo
.0..0O0.0.0.0.........COOOOOOOOOOOO
onmenmntdomdnomumtccmwummnmwnmndon
OO‘NFQFHJ‘K‘awOnNo-IFEFCIDTIHOU‘O‘ non-«ahwmnwc
00010-00 .memmmnmwmnmnhmhcnmmrrcummmwnom
ncomnomhmcmmwunconmcmmhuhmmnhmohoto
anomwnmtmhwhmHOchupducamoomawotmno
acommtmmnmmmmhdmnnoomcdmhnc~onmcnoo
anumn novmonOcmuhmnmmnuoonwnHtonmnu

mun acmomoo nonuh n nncmnumonono
N In I'III'MV Nnfl 0" 0° v-IH o-I (VI-Id
n .4 NH N

Ho—nmfi 0N co mwmmhummmhmmnmomnnnomnhnooom
IIummnmaom090ho¢o«¢«mononaowmwhownhnn
no...oooooooooooooooooooooooooooooo
Duo «an oponmnwnmncw‘h«nonunhmnhwnoa~m
comnncnocgdhwhnwnacnmmbnmwn3H6mnmmm
mmcntenannwcn—nmhcmonm0ahuwmnonwmca
manNImoncmfinummncanOAncHonnncnnhNo
HI I IIN find find. In ant—a Inleud

II II I

HwfinOONCOCOthunmmnOflnflOOnndNnOFFOOOO
I I OCOHDU‘ monnmmhonmmouncooowawnhwmnan-n
cococoon...00.00000000000000000000
cnucoohmmmnhonmmwowuncconununownnnn
$n¢wn00FmwwmmunmmnmwommcnwconOhCuop
FNUMDO" MUCHU‘CmOfltIVwOU‘ONU‘VDNNWCQOHNNF‘OIO
\o-«nP-tr OdwcmNH-ncc owocuno-mnma‘momhunono
oduuawuudmncflunwnctnnormo¢cnmnnm00¢
Hudnuudnunufl«Hauuduuunnnunuununnnnu

homoewcdtmdamcmNmOFOFOhouoononmNuhmma
IcmohmcocuNmmmcommanDmdnohcmmodnmwud
000.00.000.00.0.00000000000000000000
nncdwmhnuhwnonnwoccooumonomoanNOOAH
murmur 0mm COF‘NhF-(‘JU‘IOHQ nwnuchnonnnnnwow
HHIOII HannNNN I?IIIIIIHuu

wonmdaomwchdwowficwocnnfionmowummOchNF
Inaancmmmmn¢no~n¢o>~n¢mccocom~o¢nou~o
O...OOOOOOOOOOOOOOOOOOOOOOO00.0.0.0.
fi-«nmwa‘rm-d? “”101-0an FfiNd‘Onha I'M: O‘NU‘no-obmou‘.
madaunooammnoomomwmoccmwomcoowwodnn
omnmct‘nca-chnhgunnmntthwemucc‘conwmoc
Hudnn awn II «nwnnnmnw n a not

Homohomncccnoonncnuccncnon¢oosn¢mcNhO
Ioomwwwhmcmooanoonm«mammwwwnnwhnowwnn
0000000000000000000.0000000000000000
comwomhommhcmhmc‘ko (MONOCCC ¢Om¢nFnFOO
O0FFfinnmwoaflnm0¢oaomnfiaNfl¢0mmfiFNOQPF
mewnmwroowhnnnnmhmhhnmNnNOHouomuhow
~901Mb mmmhuw mc‘unwocoud-mcmmwc macocomh run
ounuduuunuunwnnwnc«cooohmccnnnnnnkou
HdfldwddddfifldflfiddnfidHHHHHflHHdNHfiflHHfiH

oomnwowcccnohmwnacmwchonnmhmcoonuo0N0
OOmhhonetncnnmcmmwctaumxcmdonmnuoomoo

coco00000000000000.0000...00000000000
CChCQOFnththONNdQ¢FONMmFNmOQNDnnOOd
mmmcuamhhahmmw¢cdmmohhowohnhcmmcmmwwv
hpmm«moocmnmhcnhnmhhhmtommhcuhnmcmoon
monophhmmoomauwwnncnONonNcoOGuntohOwn
ooooooOOOOCIqufidH-nndH—IHHNNNwnnnnnnct
HHddfiHdqudrfi-«fifino—Iddfifidnum“dandy-Inna"

nonnnomononoaonooonooanoacnooooonoooo
coo cancoupoooc‘ooooocnooaoo t -ooocoooooo
coocoo000.00.000.00...00000000000000.
00¢ CH1) {IwOmOv-Oh unwwmmhm IDIDOU‘OONGI'INQ "Who-I
a-n HC‘INtNFIF uNanWFF ‘ouootmmocmoomamncnc‘
FFdamCOdwhnnflmmhunwmcwhhuconnhnmnhum
«no QM'J‘FmNI-Ia‘nnm omomh 110‘ naruaflhoomuamnhhcc
nnmnuddudnnnwcnwmcnmtmkhmnomwnnwnoom
HHfiM¢ovI¢Ir~H MFA HHHH—IHn-«Hudd—cudchndHNu—I

-..-u antln mkmm u-«Nncnmhmmu-cmnc mahwmowwmcno
v-I—r-IHCIIH'I v-IHv-INNNNNCUNNOJC‘HODI'IWIODFJ

70511098

OF RESIDUALS=

SUH

A950Q98.52

SUM OF FORECASTS:

1A991839352000

SUM OF RESIDUAL SOUARED=

VARIANCE:

21503.76

STANDARD DEVIATION:

NUMBER OF RESIDUALS EXCEEDING THO STANDARD OEVIATIONS=

A62A1161Ao91

3

TRIPLE EXPONENTIAL SHOOTHING FORECASTS

FORECAST

PERIODS AHEAD

flnm05$mooauo
chuONOhhhcon

000000000000
OMNI-INnmCId‘v-Ia‘h
wmwwawmna tum”
hwnhnommmonm
mnemhmodmmhw
QC‘G‘OOHHNNIOP‘I C
HuuNNNNNNNNN

"mmcmu‘ hwchHN
way-ova

67

mama.» n Na cenmua mom copu<m Adzom<mm JdnhHZN
nwmuoa u «a oonzua can «chuck 4<ZOM¢um A(nhuzm
mmodoa 0 cu canzua mom achu<u 4<zom<um Adahmzn
hmcmo H m canxua «on achu¢u 4<zom<um Acuhuzn
_nnhmo u m ocuzua «on ao»u<u Adzomcum gqnthH
hwhmo u h canzua «om cohu<u J<zom<um 4¢~h~2~
than." u o canzua mow mohu<u 44zom<wm dqahnzn
cwwoou n m commua com «abodu aczowcum anhuzn
nwcmo u c ooumum mom ¢0h04u 4<zom<mw JathZu
fimmmo u n oo—an «om achu¢u 4<zom<un Jdnhnzu
twomo u N oonxua mom achu<u 4<zom¢um Adnhnzn
pmmho u n canzum mow mo»u<u 4<ZOM¢um Adnhnzn
«momnhn uhzuzoaxou ozuap 4<H>~z~

ooohhwwuu uhzuzoazou hzu24zmua Acupuzn

cum: um 44a) mzowqmm u o» ozouwummou tour: (pdo no woommma tn hmmmu Hi»

«#40 urh team oup<z~hmu mm Oh mpzuzoazou chcwdum n24 ozuxh .hZUZdtama u!» no mm34<> Athnzm

..coorpu: mxupznzcca

68

SMOOTHING CONSTANT OPTIMIZATION ROUTINE

RESIDUAL SUM OF SQUARES

PETA GAMMA

ALPHA

a.CDDOD0000DOODDOODDODOCOODOODDDDDD00000000000000.00000000COCOCDCODDDDCDCCCCn: _
11.1111.11.11.11111111111111111.111.11.111.111.11111111111111111111111111111111111111...I
Q¢¢++QOOQQOQ+++OOOOOQOOO09Q‘OQOOOOOOQQOOOO99¢¢§O¢§¢9+OOOQ++Q+OOQQO9994000999
ErLEEEE.LEEEr:LF.EEEEEEEEF.P.EEEEEEEEEEEE[EEC—....EEEEF.EEEEEEEEEEEEEEEEEEC.EEEEFCF35.72....
6891.359023570246993579IDS-(91‘6802Q79780135023568357802780245513579 2468026110....
22233321.333333333Q33334Q333AQRDRQR442233333333333333QRDDQRRRQQRARRRRRQE52221,
oooooooooo0000000000000000000000000...coo.oooooooooooooooooooo...-o...oooooo

59595050505050505058535050505050505050505050.30505050950505059.395050509505953:.q
0.19.6521.C11a¢fl::01«12nc3nu116zéi.0116ufic1u011.221.O1.lfic6‘1u011223c112«(Rucllfisné‘vflallnunéssCllnsfigtt .112 .
coo-0.000000000000000000.0000.cocooooooooooooooooooooooooocoo...ooooooooooo.

r. 55.55.:ODDIOUOSSSSRJDODDEC00.R4555:.Sgoocccfi_5555.500900055.:5‘35009ODIOK.SSC..5500.n.Cn.PEEZHF
ODDDCC1.11111111111222229.?2222233333300000511.11111111111122222222222231.331.1:UP. n. .-
o.oooocoo.coo.00.00000oooocoo.000.00.00.00cocoooooaooooooooooooooo000.0...o.

c..=¢::.5fi.r£ 55555555555... 5555:-.55555555555 DCDDDODDDUDDDDUODUDDCDDODDODCDCCDninn... 3...: ..
GOODnan-.90:.03009900000CDGOODOUODDDDD9011111111111111111111111111111111.1111s.11..
00....0.00..........OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO0.00.0000...O.

69

00053DOCDOODOCOUDDO000000008DDCOCDDODOOCODOO000000ODDODODDCOUCUDCDCCCDOG.UDCDCCCC
111.1111.1.111111.1111.111111111111111.11111111111111.111111.11111111111111111111111111111
ooooo00oISOQO¢¢6¢¢§o¢9,900.¢§¢§OQOOO§++¢¢6¢¢¢OOOQQ¢++§¢¢++¢¢¢4+o¢+§+¢Soooooooooooo
Er.r.r.rEFri....EF.EF:LEE915—5..EEEEEEEEEF.P.EEEF.EFLEEEEF=LCCEEEEEF.E€.EEEEEEF.EF.r.EEEE—LCCF.EEE.Lf.r.r.....r.t.r.rFLE
139123562356895680.12783135902Q5756789078012301235623‘67935639157902434567955730.1.7
332333333333333333R433A, QR QDRQRRQ2222232233333333333193333133333.3313A.RR2222222222232
oooooo.ono...coo-cocooooooooooooococo-00.00.000.-coco-0.000.000.0000...cococoa...

505.0505059505053505050505059505050505050505050.30505050505050950505050505C59:.0....95CS
7.1.0311. a: garu11fi¢n¢3011n£9~36.11:59.301.153.305»110521.0L11nénc30ulink/.30»1.19.9530112n5301126s1~nu112n.11Lllfisnsian..
ooooo00000000000000.0000.0.000000000000000...coco00000000000000.0000...o.oooooooo

55...n5..DOC5555....5000.00955555SOCCCOCSS:.555000CCOS555550CDCOUSS-355500900955:“SSRhVODCCCS
9911.1. 11.111111122222222???233333.13.»COCOC11111111111122222222222233331....DD CDCnhh.111111I
coo-opoo-0.000000000000000...coo.oooooooooooocoo.oouooooooooooodooooooooooooooooo

SSSErSREEJRR 55....5555555:.555555555553903C39DC0390300n.30390000309D0099309555: ,c-.r~;.:5r..5c.c .5
11.11111.111111111111111111111111112222222222222222222222222222222222222222222222222
ooooocoo.oooooooooooooooooooooooocoo-00.00.00.000oooooooooooooooooooooooooooooooo

70

Ca.0009000000000000900DD00COOOOODDDDDUDDDDCOOOODDO0000000000
1.111.1.1.1.11.11111111111111111111111.111111111111111111111111111.
0o0+6.9906.009¢94¢¢o+¢¢¢+¢¢+6§++¢¢¢o¢¢9¢¢ooo¢¢¢¢§¢++¢¢O¢¢¢§o
Eff???.EFFEEEF.EEEEEEEEEEEEEEEEEEEEEEEEEEEEF.EEEEEEEEEEEEEEEEEE
0.6.1.239013.51653568245790233‘56R55678567990789013831234012356
2233323333333331.3333339222222222222222223222333233333333333

0.0.0.0....0.00.00.00.00......OOOOIOOOOOOOOOOOOOOOO0.00....

053505050505359505950505053505050505050505050.3350:.050505050
11221.6.1.1223C11223C11223011n.23311223C111223911223011223C11223
...coo-o...coo-o.coon.ooooooooooooooooooooo00.000.000.00...

5555:.3900.CCSSSESSDDODCD555555000090555555000090555555000090
111.119.229.2222n¢2221.3‘.3330cacn.01111111111112222222222223333.33
00.00.0000.00.00.000.000.oooooooooooooooooococo-000000.000.

... .55...5c.....555555:..:9.55555555305.9903330C03030003h.00.909090003100003
22222222222222222222222333333333333.333333333333333333333333
cocoon-.00.0000000000000000000000000000000000000.0000000000

THE OPTIMUM SMOOTHING CDNSTANTS ARE:

.05

GAMMA

.05

.30 BETA:

ALPHA

INITIALIZATION PHASE

OUTPUT OF THE

RESIDUAL

L

In

TREND SEASONAL FACTOR FITTED MOD

psnnnuznt COMPONENT

OBSERVATION

PERIOD

71

omcmmmnanmhumchwnmmnmhtw
o«ca-Chocmoooor~o~onma~mmmmcm
00.000.00.00000000000000
CM€mQ¢aHCHF~ONDHFODO~NNFDn~DCh
«marsh-mommcmmmcwmwnnbcwm

ommflouxnmmndhcwhcwcma‘m I C

unmomuann humwnnummoc O

ITII—III ?II—¢~—4 H I

I

ocommmnonmnmmch—cmmwh—onco
amatehucmomnmhommnonccncm
000.00.00.00000000000000
Chic ooahcmnnomomamcmoannm
«dcmmr-hwhnmonwmmchwnodd
«mmmnmwowumcwoomamcmww
owwowawhnmmwucom~m~mumum
«Nantunudcnccauuumnnnchhm
HHHHHHHF‘HHHNF‘HF‘H Hv-Iv-Iv-Oo-‘HH

hmmahhmm mmoosmuouhmmmmm
mmoomwmnoncc monommm—tan
cocooooooooooooooooooo

NH HOMO-I "H "F."

00
mo
0 o

nfl‘oomwor-mnnmcm—owmmOOva-tw
I."CLOT‘QF'OFOH‘DF'IFADOCU‘IDOJCNU‘F
ooooooooooooooooooooo.oo
\DU'NInhuno-«r.mmhmmcdmmmhmmown
«mmmmu-mohmmdoammOh-«Nnomm
«...—a. hgmcr:nn¢ra¢.o\fimmv~munr ax
NNNUH—ouvaHHHHM-n Mono-«HHNNNH

hmmmmoonsoumhnomwommhbmoco
«Hutmcwmncmmnmnnhmwnwwoho
0.000.000.00000000000000
(FF wcwuc-Qummcwmfim(.wnchmmw.
amoHchauumr-‘O‘NOIDmmmmnhmhm
ONcmmwdcdcmmnc'honomhwumn
°¢P~u1nCJCOJNCanN~HF~ tmdhnmhh
NNNI‘JNNCJNNNNNNNNNHF)?‘IDU‘HDID
H. I .4. IH. IvI'IHHfifi'IcIrIflrIquvIHflv-I'I

oooooo cocoooonooooocoooo
GOODODGUOCoQOCI00000000000
......OOOOOOOOOOOOOOOOOO
C? 3.444;) ODI‘DO—dfi HnNOH-Dh-BFO‘IDIDO
ONO—INNQ NmFONnHMBFm—domwm
hhnomc wdohnnnc‘whmmm'afih
mo~0anmNHmmemwmhaa‘nmm—om
0..ruuo-tuv-«Hnnnmmcwoouncnmtwhh
fi'IHHHfier-Io-Io-Ov-IH HHo-Iflflu-AHFOHHH

«arm n wr‘u‘o-c ammo wwhmwvv‘Nn‘I
HflHfi—IHHHHPInfllIvhHu

79.58

AVERAGE RESIDUAL=

STANDARD DEVIATION

1909.82

OF RESIDUALS=

SUM

9718.70

90453063.9O

MEAN ABSOLUTE DEVIATION

VARIANCE

7620.78

1

NUMBER OF RESIDUALS EXCEEDING THO STANDARD DEVIATIONS

OUTPUT OF FORECASTING PHASE

FORECAST LEAD TIME IS I PERIODS

= 12 PERIODS

SEASON IS

LENGTH OF TH

SEASONAL FACTOR

TRE

pERMANENT COMPONENT

DHSERVATION

PERIOD

90~nwuhomhom
lwwwonmeHnu
0..00...00.0
H01 "000-.

wmnhnmmwmdwo
momnmcwoonow
000000000000
ocowcomnmnmm
ocmnreowsnno
Ohmhomcaommm
"doIv-Ors—Io00-0H0-Ar0—I

0 COFOrIan-«Dw
In WOOD—oonh‘DU)
00000000000.
”NF-OJINNWNO-Iznrn
DmdMJNflNO‘FQO‘
nmuncnmnuor‘m
O-OOO mochcouom
nmmmnmmwohhw
Hfifimcd.1NH04HH

000000000000
ooooooaaonao
00000..000.0
00¢ Na!" “Omar—c
ocmOmmmmnc-«h
«comhumnhdu
saoomzrvapco
Nrocmw-nnmne‘c a.
Huuunnunamuu

IDVDFCLO‘UMCJI'OCIOAD
(‘JNNNN'OIOI'N' Inf".

TRACKING SIGNALS

ERROR

ERROR

FORECAST

PERIOD

OTHED ERROR

SMD

CUM.

72

chownnpoowwo
oun«~w~~«onn
..0...0000.0

IIIIIIII I

04) cunnmmc 0‘ on
Owwwwnanwmnc
0.0.0.000...
«wnwnnNnIIN
IIIIIIII I

thmwmhwmmnh
OHOOF NutU‘nOIDm
0000000000.0
0-«1 mmunwmruoaa
nnhwwmnwmnco
nnumcwnn I OOH-A
nunmwcn "fit
7"". I Io-I 0n (:1
I

«umnnohtmwmh
Unowhmnonmnn

0000.....0oo
haomeOOQmoo
OOFFNHHMONQ
hnwhunnmnnmc
omnhunOthmc
NCDCBJDmnmnc
fiddflHHHfi—H—IN

WOFwO\C-HCMCIDJI
NNIVNCOF’N’IFN'IF. nn

-2256.70

AVERAGE FORECAST ERROR

'27?PU.AI

SUM OF FORECAST ERRORS

VARIANCE:

1153A.AR

STANDARD DEVIATION:

I33OAAZ9P.81

HINTERS METHOD

FORECASTS USING

FORECAST

PERIODS AHEAD

NCNmnn0h¢wm¢
NFOJMDIDQO0HFOI-

00..000.0000
onumcnwnunmm
whnoflcthmwuo
@homwmouthoc
wanQOQOCOWQ
nmwwflmphhnOn
nunununuwwwm

HNmtmwbuaUHN
an"

73

METHOD ANALYSIS

METHOD MEAN SQUARE ERROR
SIMPLE REGRESSION 335797677.41
SIMPLE MOVING AVERAGE 087215093.27
DOUBLE MOVING AVERAGE 702234124.SC
SINGLE EXPCNENTIAL SMOOTHING 493630736.70
DOUBLE EXPONENTIAL SMOOTHING 392398257.83
TRIPLE EXPONENTIAL SMOOTHING ' 427980981.49-
HINTERS METHOD 127049974.27

USING GIVEN PARAMETERS. THE BEST FORECASTING METHOD IS:
** HINTERS METHOD **

74

CHAPTER IV--NOTES

1William G. Sullivan and w. Wayne Calycombe, Fundamentals

 

of Forecasting (Reston, VA: Reston Publishing Company, Inc.,

 

1977), pp. 113-120.

2Douglas Montgomery and Lynwood Johnson, Forecasting and Time

 

Series Analysis (New York: John Wiley & Sons, 1973), pp. 278-282.

 

CHAPTER V

SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

Introduction

 

This paper attempted to create a multiple forecasting tool
that has the ability to handle various data sets associated with
telecommunication properties. The multiple forecasting system is
intended for use by both professionals and students, especially those
interested in acquisition finance. The forecasts generated might
be used as part of the financial analysis required by both investors
and lenders in their determination of property's potential. The
forecasts can also be used as part of managements ongoing financial
analysis for an established property.

The chapter begins with a summary of results and a discussion of
the model's limitations followed by conclusions and recommendations

for further study.

Summary of Results

 

The data set used in this study consisted of monthly radio
station revenues over a three-year period. The radio station, located

in the Midwest, is in the top 100 markets and has more than five other

75

76

stations competing for advertising revenues in the market. Using
established forecasting theories, discussed in Chapter III, projections
of future revenues were generated. Initial calculations were validated
manually. Then, using a computerized multiple forecasting routine,
developed in Chapter IV, monthly revenue forecasts were generated for
the next year.

Seven common methods of time-series analysis were used to
generate multiple forecasts. These methods were used because each
has strengths and weaknesses in handling various data sets common to
broadcasting. In addition, the mean square error for each method was
calculated as part of the "Method Analysis."

This method analysis, on page 73, shows Winters' Method as having
the lowest mean square error and therefore providing the best forecasts
for the given data set. This is evident earlier in the results which
showed an average forecast error for Winters' Method of only -2,256.40.
Compared to the average observation of 142,439.00, the average fore-
cast error is fairly insignificant.

Other checks of forecast accuracy included a standard deviation
of 9,7l8.7, a variance of 94,453,063 and calculation showing that there
was only one residual which exceeded two standard deviations. The
variance measure provides the operator with a mathematical index of
the degree to which the individual observations (revenues) deviate
from the mean. The standard deviation represents the given distance
of the observations from the mean, and is useful in the examination
of residuals. The fact that only one residual exceeds two standard

deviations in the Winters' example indicates this particular method

77

does a reasonable job in tracking the observations.

Since Winters' Method appears to be the best time-series
analysis for this particular data set, one would conclude that the
monthly revenue observations follow a seasonal trend. The strength of
Winters' Method lies in its ability to track seasonal variations and
formulate projections which also follow similar seasonal trends.

Like other exponential smoothing methods, Winters' Method averages
historical observations in a decreasing (exponential) manner. However,
Winters' Method adds a third smoothing constant to the forecasting
equation to account for seasonality.

A second look at the method analysis shows simple regression with
the next lowest mean square error. While the data set follows seasonal
fluctuations, as indicated by Winters' Method, these changes do not
appear extreme and the data seems to be increasing in somewhat of a
linear manner. Linear data is best handled by regression methods of

forecasting.

Limitations

 

Results indicated that, for this particular data set and using
given parameters, Winters' Method provided the best forecasts. This
is important, not because of the particular forecasts generated, but
because it demonstrates the progranfs ability to project data using
various forecasting methods. There are, however, several limitations
to the program which need to be discussed.

First, the user must supply several parameters such as the

number of periods used in moving averages or the exponential smoothing

78

constants. Changes in these parameters will effect forecast accuracy.
Likewise, the user supplied boundries for Winters' optimizing routine
can be changed so the resulting smoothing constants alter the fore-
casts. Therefore, some level of expertise is required to operate the
program.

The second major limitation involves the data set used in this
paper. This data consisted of monthly revenue figures from a single
Midwest radio station. Not all data sets have monthly observations,
some consist of quarterly or yearly observations which would change the
results. Monthly data tend to exhibit a seasonal pattern and yearly
data will most likely be linear. Similarly, only one station in one
market was tested. Different market sizes, conditions, and character-
istics might also alter the results. Since time-series analysis is
based on the continuation of previous market and station patterns,
changes in program strategy, not an underlying trend, could cause severe
fluctuations in this historical pattern. Likewise, changes in the
market, such as new competition being introduced or stations going off-
the-air, will affect the outcome.

Finally, only "revenues" from a radio station were used to test the
program. Other financial variables such as cash flow and expenses may
have their own unique forecasting needs and limitations. Likewise,
forecasts of non-financial Variables such as ratings and shares, should
be tested to see if the program can accommodate these data over time.
Other media also need to be tested in the model. Observations from
television or cable properties may contain characteristics not explored

in this paper.

79

Conclusions

 

Despite its limitations, the program developed in this paper
is a powerful and unique forecasting tool. Unlike standard fore-
casting routines, this program combines several methods of time-series
analysis in order to handle various types of data sets without having
the operator develop a forecasting system for each type of data that
needs to be analyzed.

This multiple forecasting system also provides the operator with
various methods for analyzing each individual routine. In addition to
the mean square error calculations used to identify the best routine,
each method is evaluated using measures of variance, standard error
and the number of residuals exceeding two standard deviations. A key
advantage of this forecasting program is the ability to analyze the
accuracy of each routine. This self-analysis adds strength to the
multiple forecasting program, and increases the comprehensiveness of
the program without sacrificing the ease of operation which is another
of its strengths.

The computerized multiple forecasting routine developed in this
paper, serves as an adequate base upon which management can develop

a budget which accommodates previous performance and future expectations.

Recommendations

 

The limitations discussed in previous sections highlight the
need for further testing of the model. Likewise, the limitations

might be reduced as the model is expanded and refined.

80

First, the model needs testing using numerous data sets from a
wide range of media, markets, and properties. This must be done to
insure the model's comprehensiveness and utility. As unique data
sets are introduced, the model should react accordingly and generate
unique forecasts which must also be as accurate as possible.

This accuracy can be further enhanced by proper selection of
model parameters. Iterations using various smoothing constants and
moving average numbers need to be done in an attempt to find the optimum
parameters. However, this process could be tedious and diminish the
usefulness of the model.

To alleviate this problem, it might be possible to expand the
model to include optimizing routines to generate smoothing constants in
a similar way the Winters' optimizing routine provides the Alpha, Beta
and Gamma. Further optimizing routines would help the model react
to many different data sets. They would also strengthen the individual
forecasting methods contained in the model. Currently, the optimizing
procedure in Winters' Method gives this forecasting routine an advantage
over the other methods in the system which suffer without the optimizing.

The time-series techniques used in this program are essentially
"short term" in nature. They provide optimum forecasts for periods of
one year or less. Therefore, they should be updated on a monthly
or quarterly basis. This ongoing process should be part of a station's
budgeting procedure. The information provided will let management
examine previous performance, continually update the forecasts and

modify them in light of new information.

81

To further enhance the program's usefulness, the language
needs to be converted from Fortran IV to Basic so it is compatible
with smaller computer systems. This would make the program more
attractive to owners of smaller broadcast stations.

There are other options that may be included in the program
to make it more appealing to these smaller station owners. One addition
would be a scattergram option. The data in question would be plotted
so managers can graphically see existing trends. This visual plot of
data over time may be helpful in the identification and selection
of the proper number of periods to employ in a moving average, or
what constants to employ in exponential smoothing. Intuitive decisions
can then be made regarding which forecasting method generates projections
that seem to fit the data set in question. The program might also be
rewritten to make it part of an interactive operation thus eliminating

the need for computer cards

BIBLIOGRAPHY

BIBLIOGRAPHY

Chapman & Associates. "Using a Computer for Investment Analysis."
Broadcast Financial Journal, 7 (January 1978): 24-35.

 

Dickstein, Barry J. "'True' Station Value is Key Ingredient in
Broadcast Financing." Broadcast Financial Journal l0
(March 1981): 16-20.

 

Fildes, Robert. "Forecasting: The Issues." In The Handbook of
Forecasting: A Manager's Guide, pp. 89-95. Edited by Spyros
Makridakis and Steven C. WheéTWright. New York: John Wiley
& Sons, 1982.

 

 

Granof, Michael H. Financial Accounting. Englewood Cliffs, New
Jersey: Prentice-Hall, Inc., 1980.

 

Hague, Lee. "Acquisition Financing: An Overview Update."
Broadcast Financial Journal, 8 (March 1979): 19-23.

 

Hanke, John E. and Arthur G. Reitsch. Business Forecasting. Boston:
Allyn and Bacon, Inc., 1981.

 

Ingle, Kay 0. "Radio Entrepreneurs Fill the Airways." Venture, (1979):
62-64. ~

Makridakis, Spyros and Steven C. Wheelwright. The Handbook of Fore-
casting: A Manager's Guide. New York: John Wiley & Sons, 1982.

 

 

. Interactive Forecasting. San Francisco: Holden-Day,
Inc., 1978.

 

 

Meier, Robert C., William T. Newell and Harold Pazer. Simulation in
Business and Economics. Englewood Cliffs, New Jersey:
Prentice-Hall, Inc., 1969.

 

 

Montgomery, Douglas and Lynwood Johnson. Forecasting and Time Series
Analysis. New York: McGraw-Hill, Inc., 1976.

 

National Association of Broadcasters. PurchasinggA Broadcast Station:
A Buyer's Guide. Washington: National Association of Broad-
casters, 1978.

 

 

82

83

Nielsen Station Index. "Buffalo, New York." Viewers in Profile.
Northbrook, Illinois: A.C. Nielsen Company, May 1983.

 

PK Services Corp. The Primer on Radio Station Investment. Carmel,
California: PK Services Corp., 1979.

 

Poole, Harold. "What's Your Station Worth?" Broadcast Financial
Journal, 8 (March 1979): 10-12.

 

Quaal, Ward L. and James A. Brown. Broadcast Management. New York:
Hastings House Publishers, 1976.

 

Sansweet, Steven J. "How to Buy Your Own Radio Station." The Green
Pages. (1978): 54-55.

Schall, Lawrence D. and Charles W. Haley. Introduction to Financial
Management. New York: McGraw-Hill Book Company, 1980.

 

 

Schrieber, Albert N., ed. Corporate Simulation Models. Seattle:
University of Washington, 1970.

 

Spiro, Herbert T. Finance for the Nonfinancial Manager. New York:
John Wiley & Sons, 1977.

 

Schutz, David E. “Is That Station Really A Bargain?, Part II."
Broadcast Management/Engineering. 14 (August 1978): 86-88.

 

Still, Richard R., Edward W. Cundiff and Norman A.P. Govoni.
Sales Management: Decisions, Policies and Cases. Englewood
Cliffs, New Jersey: *Prentice-Hall, Inc., 1076.

 

Sullivan, William G. and Wayne W. Claycombe. Fundamentals of Forecasting.

 

Reston, Virginia: Reston Publishing Company, Inc., 1977.

Ungruhe, C. David. "A Comparative Analysis of the Communications
Media." Valvation Reporter (First Quarter 1979).

 

Wheelwright, Steven C. and Spyros Makridakis. FOrecastinq Methods for
Management. New York: John Wiley & Sons, 1973.

 

 

Weston, J. Fred and Eugene F. Brigham. Essentials of Managerial
Finance. Hinsdale, Illinois: The Dreyden Press, 1979.

 

Yadon, Robert E. "Application of Forecasting Techniques to the
Telecommunication Industry." East Lansing, Michigan: Department
of Telecommunication, College of Communication Arts and
Sciences, Michigan State University, 1980.

Zwass, Vladimir. Programming in Fortran. New York: Barnes & Nobel
Books, 1981.

 

APPENDIX

84

PMDMF

=1

CPT

7II175

PROGRAM DELUI

1.6" 6:1. I
ot‘DIolIb,
...R ...-at Tau

EF2H21U

I 9.0066 I)
,D‘F“)o
1.2. 620?.»
66MIT ICS
‘IDO. I).:l.
[Brit—EIII‘
I". IIZESI
I. IIGL...‘ IR

OUTPUT)

:S‘u‘, 9‘
)2EIA2)F
1.... Inn-.150 I
61.00.05 I100,
(Afl.¢u)s.:o
0U. 6.5.53.5...”
SDIDGSAS
X IAEIFHI
DIM. IS I Is
ISIFIIS
..ZE ’6E62721. I
5 IS 1!. I5 I66,

TE ET’IIIIQ

T1 -
SIMSEDESIMSETESIMSEHIONEMAAIONE

I

E

I

p

T

F

0

I

INPUTITAPE 6

UN...» .tltFnE. III
P05 II. Ire-5.))...
T I" Irv)- I210
U... I 0520.16.60
UNA TOS2II5
IBM ISISEORI
TIS IEBEISOP
U2: .bY [SOSFF
FMS A. I O'CSESF
NS" 7)... 131E I
I I I IEOXILFD)
.IIoR 016620 I '0

NE IIIGF’ID
ASS GSA... Izlt.
U I" IEESISEI
LT I ‘0 IEZIIR
E I85 IISESA I

IM026 IDTDR 0 0 0 .0 JD
HRAEIGISERZ .D 0005: 0 0 0 0
AEPNSISZS IO IC:O: : :0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 00000
RG DNA—L DEIFD: 7 ..C075 0 0 . 0 0 0 0 0 .OOCODDDDOCDDOCDD: : .. :
GEL ICE. to ($2 IIYU’SSXAOQW:ID...C~.0: : : .. : : : : : : : = : : : ...- 13.3. D
UTA—5M5 I1. I5)(u MM TIMI... .... : : .... :=0123955121.“557991.111z..

RNEBI I)SI(1FUUUDDUU123I§675911111115555555555555XY
PIRMDIZAn‘S bFSSSSSSSSSSSS55$R.S$sssssss5555555555583
0 0 0 0 0 0 0 0

10
1
20
25
so
35
49
.5
0

DATA POINTS

READ IN NUMbER DF

CCCCC 7ccc

AND CORRESPONDING DATA

READ IN PERIOD

E
G
A
Q
\I E
J V
I A
A...
= G
1. N
I T.
I V
T. 0
I) H
70
I 0 R
)Ru 0' 0
IF 1 F
A. I 9
xx 71 R
(INS E
) IVY N...
$5.1... H
01.1... IE U
I I‘IIU N
0050! (N
1....(A1AT. 0|
OIIDNQTT U
0111.03. AV 9
:IIEOODO N
JITP FmJUC 1.
a» 1.
1. ....CCC
K. 1.
6 7

FIN “05.569

85
1 PHOHP

OPT

74/175

PFOGRAM DELUX

0 0 I
0 0 I
0 0 I
0 0 0
0 0 0
0 0 S
0 0 I .
0 0 I R
0 0 E I 0
A I I U I R
T 0 0 L I R
A 0 0 A I E
D 0 0 V 0 0
0 0 S I
.L 0 0 L F. X N
H 0 0 A I e o
T 0 0 U R I I I
0 0 0 T E 0 2 S
H 0 0 I C S R 0 S
S 0 U 0 0 I A D I E
N R G 0 0 I F. R I R
0 F I 0 0 X D M R F 5
I00 D 0 0 B N I E I E
TEE D G 0 0 A T 0 M R
All E I 0 0 I, I 2
LFI P L 0 0 I E. A X I .L
UIHH.U R Au 0 O .Ax U I ?r I9..L
CCIDL H I 0 0 .. H L F I I I 0 P
LETEE M U 0 0 IU A 0 0 0 IO M
APPIV A B O Q Is V 0 cl 01 I
CSOFE S I 0 0 I0 6 0 S SF S
D ID I D 0 0 TM I7 N N A EI
A LEE...» I a O O 0 6 I 0 c Ira N
E ERREE A I 0 O N V [D T. I E )9. I
Hr. DAAPR T L 0 0 05A HE S s R I I
A3 0 SA E B 0 0 III TO! A S 0 I2 5
A M55 3 I 0 0 S . STA C E F E. L
SM TTES U U 0 0 SEO L M E R 0 ID A
D NNNRE I A 0 0 ENS ATI R G.I II U
0: IAAAU T A I 0 0 RIM URI 0 E R IF 0
I8 TT L L H D 0 0 GLM D S F R 9 II I
R SSSSSA I P A 0 0 E U IEE I TX S
p10 ritNNEV U L I I 0 RNS SU E E I $3 E
PL IIOOU I. A I. 0 0 I 01. ...—L" L L V .L I R
U RRCCLL I H A 0 0 I EI/ RAE P P 0 V2
F0 EE AA N I I 0 0 I2 LSI VE I M I I. F
OH SSGGVIN K O 08 0 0 I0 PS) D H 2 T I X )0 O
S NN TO II 8 83 0 0 I IV. MET N77 0 L S 7 II
R. LEIILIS $3 I II. 0 0 I I0 I IR" A .L 0 U 0 I IF 5
ET MMHHANA KI 5 5 0N0 I I III SGU DB I) M 0 0 VI E
9.5 TITTII'L I2 I I0 0 00 I 20201.... [S SE III I 0 X In» R
MA TTODT S II 0 OT 0I0 YIX050SII FR.) ETE III I 0 0 )2 A
UC ODIE NI A A I 050 I) GYG0Y0XXI O XX UAC ITT2 X I I II U
NE FFMMNHFE II [IE0 I 050 II VDVIDIDID RGG LMN X550 3 A A I2 0
I R ODSSITOM H2 RORGOOI 0E0 II A0AI9I00S SAVV AIE .EE0 I5 8 3 II S
3 E0 T I NI I0IIABS 0R0 YMNN .7.IOIOYI TEAA VTR 377) 9IISII II
. HF I) HHFFFFHT I3 OAIIIII .G. doolldIDIYSXSXM NNI. SE J.:.I 91205IJ6X F
5 T 92 TTIIIIT 3I .F..OOD 0E0 IYMVMIIMIDYDXMU EI.B DEFI IAIII 9HI/1/II2 0
F E II 65 60 R2 090080.85 0R0 2MMMM2IUI:D:DUS ILYI EzF 2:IIEEII II 012 I9...
I NH II NNII II ”A II ..LIEF. IIIU 0 0 :UUUU:YSMISISS: C x. III—L :III:UEI6I.DI:6IUH
7 IT 57 EECIDIEE 5TTOT00555N 050 ISSSSI:::I:I:=O IEMT AIDM IIOTINITITITIITNU
A (A LLIIIILL (ALSASNIIII 0L0 :::: IYIIOIOYS FLUG MI:I (SzIIFAEAEA CAIS
M DT DM DM:KHKKDDDT 0P0 ZTXYXSIDIOSOSXX FPSV ITIT ATTIITTMTMTMFTuT:
R AA AR .. .. : : .. : : : ARTIRIIAAAN 0 M 0 Mn 35 IMISYSIMM [MIA TSI SSIJNIRIRIR IRV...
0 EH E0 HISSNNHT EOLFOFFEEEO 0I0 OUUVVOYUXYDXDUU 0.1:: SEIT DEEISORDP OR 00000....
F RT RF NNKKKKLL RFXIF IIRRRC 050 DSSAADDSDDSDSSS CSBA EVER DTTEECUFUFUFDUFCS

8
9 3 0 3
O CCCC 1.Cccccccccc O. .5 Iccccc 2 ..JCCC CCCCCC Q

999

2 6
1. 1. ..c rurb

80
as
so
95

100

105

110

115

120

125

130

135

140

145

153

86

“069590

FTN

PMDHP

=1

OFT

74/175

FROG: M’ DELL‘I

R N o. o
.b C I 0
... I . .
I R I T t O
2 A O 0
: E o I Q o
S L c V t o
R F I E o I
0 N F D a t
R I I o a
R I S a n. n o
E 2 R 9 I
O F = A t i
F I 0 N 3 a I
O I O N a I
F B I A O O
H I I T T a a
U I I A S o o
S X I O a
n I : 5 V 0 0 a
I 2 v. I E H a o
X o 2 D T I o O
5 I E o I t a
I .... G 2 D G S n o
2 F A I R N T a 0
o I R F A I S .5.
9 X ..L I 0 1. D A I on... S
I 2 V I N o E C I II. E
F I A A R E E I CHI 5
I I I : T T C R 0 0T. A
X I N S K X 0 T .0. R
2 .. X D I : E F S .0. . E
I D 5 I I R A 0". V
a F. I S X T s N C Is. A
R 2 S I K L 0 E o n
: A o E I I A I R 0L. 5
S U S R 2 H U S 0 0A. N
T 0 F G o D D S F OI. I
S S I E A T I F. I 0T. V
A I R I S S R I oNo 0
I C R F o E G X I .E. SSH
c E O = E I .l R E 0 I IN. E
o R R X L L R I I to. 567.
I O R P = d F I RI .P. AAL
- F F. E H E I o ..L n 02 OX. RRB
J G I C I L D F 0 0E. EEO
I F FYA S N I R P 0 62 o o VVD
I O 05R. DA E E H I E1. ID. AA
I VE 7. TI I .h I I R RF ON. H
2 5H PAV 0 SR R H S I E II cA. GGT
. IIU U IA I IA 0 U I I P IX a . LNI
I o SSS SXn AQPV I 0 RN I Z n IE .5. I19
I I E S In In 6 I8. 0A9 0 D T. X X a IX I I at... VV
II I VIOII OJIVXIIUVI 0 TI KI Ce 8 9.. X8 [2 .6. OUT
IOII ARISX SXAQAXIIX 2 JS IX I5 I OI? I II tAc HHS
ISIQ 0 A~I9 I9I3I9F39 .0 I 0 Q9 0 I Y ASSV. o I OR. A
JTTIS JVI73I538 I63 I03 IT2T 01.. II B = 5 IB 5X 9E. EEC
ISSFE J . (SI I23 III... I. 3 I 0 5:5 3 I 5’ .. I5I : 50 0V . LLE
2...»: O 97.! IT 0 II 0 II II II II 0 0T. IE III II I I III I6: 0A 0 PUR
:YYSIUESRIGIDGIéTéI:EIOTD IUéIIEI I6I 6IU I a HUD
IooISNlSOIITIITIAITNIT.SoOINITIITNICIRITOIITN .5. IOF
10.5...ISIS:r.AFEAEHEAOEAU..23IIEA IEAO Av2..nuEAI:EAI 0N. SD:
($5....T:: :RTH ITMTP.TMITM :H:3ETTMITHTN5IFTHSITHT oIo ....A
::5IVE?3§IRXIRI3IRSIRR33 INIR IR:: I3IR IIRN oVo AAH
. AIZISOVATSROZD ORFR OSFOTTTDFORO..ROXYOIEPOOIROO n0. HHD
355:.5CAVSM HF IHFU HF“.HFKSSDICUFSUFBBDZRUFDZUFC an... SD...
9 O
3 r. A. S a. 6 PC
7 5 h. E P. 3 fl 1. 2 5 5A
6 I 1. I 3 ..J 3 3 .3 5 c. SSCCCCCCCCCCC
& O : 0 5 0 5 0 5 0 5 rd
5 6 .t 7 1 8 e 9 9 o 0 I
I I I I I I I I I 2 2 2

2

t

2 o
H I I
1. S I I P
P I HII N
N II UJA ... I
I H... NI" 9 H
2 H 59 IAS 2 U
0 U z" IIMH: o N
HI IN HIEo¢SSIEI 1.:
2U" H: TUI2::IUH HI
ONU UICn ONFNIAINU U C
N:N1.N oSHISQ~IH0INI.rH5 I
:1... : 38.36.00'! .. : ISST : = :4)
INN...» : :NISARANVI? :

PUUNM 00. OMOM NHCHOUVHOH
NNNSSDSDSCSSSFSCNDDOD

. u
5
4

CJ

215
223
2
231‘

9b

87

FIN 9.8.56Q

0PT=1 PHDHP

741175

PRGBRAH DLLUX

2/INUH1-l)

)
o
.

=DHIODM2
A(HOIONUHI)
O
D
)
H

C9 NH"): ..ION
6H 1001).)‘51
QDT .. .. (7415A?

.. V1.¢Q(CHHV
0M OHHHABDDO

E
L
B
U
0 R
D O
F
R
O N
F o
665 I
NNNN T
11.1.0 ‘
HHHI U
vl'lvlol a
000‘ E
DOOU
HHHG 5
SSS—L N 65
I NN
LLLG T. 11
All" 3 NH
1111 I T1
TTTT C 00
NNNS E 30
r..Lr.A R "H
NNNC 0 SS
COCE F
PPPR LL
XXXD E II
EEF H II
T TT
[Eff NN
LLLH N E:
GBP'I 1. UN
NUT. 0°

RRRS [I

000.! VAN—LE

FF'N CTLL
E

CCCI FOUI
IIICGFHOR
TYIVIINLSDQI
SSSFIO
IIFHCLHH
ololT—LT I'lvl
AA‘OOEIII
TTTCOH'IUU
SSS HTN
[5 ET?
DDDH [~55
EEEVLRO“
HHH “APCC
olvl'l—IY. XE:
OOORTC£RR
OOOANT 00
"NH EOEFF
SSSPNBL: ..
._ .. ._ EOvIPSS
55$ 9? 091......
EEE‘XARDQI

DDCDDDNHFFC 537?..LololFF
G.
.b 5
4 QCCCCCCCCCCCCC
.. c .... 0 5
3 § Q 5 5
2 2 2 2 2

P
L
I
o
o
8
.
o
o
1.
I.
.
t. \r
I .l
( Y.
s ‘
E S
S .l
a 1
) O
‘ ‘l
H I
P 1‘
L S
‘ E
o 0
o a
‘l ‘1 5 o
1.. \l 1 o O
\l o I c O 2
1 I H I 6 -
o 1‘ P n! I. .1
I s L s,‘ 1
1| E ‘ E1. - 2
S D . T.,)s I
..L O O 0"”: \l
S ‘1 1 ’(215 1
9 I 1- Ans.“ .
) H I HE'S. I
) P I 97,52 (
1 L H LQATO C
c ‘ P ‘IJHOI 'I
Y. o L .IP’) 0
..I o I .1 OCLI) \a
S 1.). 1. 151.". 1
E ‘1, . «Pb-PH .
S 0‘) 12 oDoLP 12
. 2 ’81 ‘0 ’01‘L ‘0
\l . IE‘ 8. 10‘0‘ a.
I 0 ‘05 E) (300. T)
I. ‘1, sop... 97. S. 030 01
Us 11 [)0 \ll‘ E’O...‘ \l‘
I. on. ST.- 15 DI‘ 0‘ «is
o 1.5 \a 0" ..L ol‘IQI ..L
A JCE J AS! JID ISAC! JIT
DJ” .55 ()JHEC OCF )JHEHOH OCF
20F 35.? $2 OPSS 3A.. ZQPSP)P 3‘:

(2L :5: ECZLOE :E) C2LnLIL :T)

'- ...-5512).!5'2‘ 05:121-057..“ OA“—LI :IE
=I:U )IU::1:2IU ’IU:I=3IS(U )(U
‘0 )NOXCNR’ ).. ..NUION) .1: ..E..N0!0N
16707.1(010151))12‘51111)’0)13(SI
(0(TQSSTF(5(IIT§SST(5(IIoITQSST
S S“ 7.5MSS 5“" —..-..VS S‘()(‘ EDD-v
EDCOOSEOEECEABOODDOEOEABACOOTYO
SDSCDFSCSDDDEECDFFCTDTTYmTCDFFC

D .U 5..
6 1 5 2 1. 3
U . E. U 5 “ccccccc
o 5 o 5 a £6 0
6 6 7 7 a a 9
2 2 2 2 2 2 2

E
U
LL
‘A
'1.

T f.
LN L
IE P
UN .1
To R
C? cl
“x

F. N
O I
N...

‘L ..L

B U
DU L
E0 ‘
To U
‘

"E L
IL A
7.5 U
SN .l
ET. C

S A
N
ED D
EN N
HI I
ol
[5 D
8...... E

5 7!
E. A
CR N
NC I
..L' cl
R. s
F. E
F5
F” N
I! E
0V [5
:0 UN
5" TI.
E [H
Dr. 8....
EL O

08 [0
SU CH
[0 NS
50 ..L
.5. RL

9 O [A
‘EGFI
”LNFT
DPIIN

2 ,2 ‘51.)9.

\l. I. 1.140
I. (I ‘0 ‘0
‘, A’ 5.15,
A»! "1 7.7.7.1
H! 0!. 5(0(
5‘ F‘ FSFS

J . H J . In . F. . .L
"s 2 0,0 ,5)“.
"IE 9H1: JIEIE
2U(.. 2U‘: OI... 0.:
ONV’ 0 NY.) 3'3Y)
1....IE1....IE: :T...1.
HI’(UMI’I‘UI")‘

U IONU ION 101n-
NII‘SINsrCSIS‘SCS
..1AAY..Q8ATQS\.SS
q HHVU. ”i” ......L...
UOSSOUODDOOSSDD
NDEECNDEECDEECE

1. 7
b

295
360
305

FTN 4.89569

88
PHDMP

OPT:1

71’175

PROGPIH DELUX

S D
E T :
R s s
I E L
1 R I
X I U
I 1 D
0 II T
I 6 T s T
L O 2 E 2
I I I R I
U T I. 0
D s 1 F 1.
T I TF 0 F.
S C T. T O
E r. I! I” l
R T R” 09. T U .1
I 2 0 .30 2 c. O T
9 I F .I2 I I I I
I 4 I H I I. 9 S
5 1 T 1. T 02 1. T 1. I s T T
o TF 0 O an E1. F n. 9 5 T S I
T I 1. O I R 6 9F T I R 9 I D
I T .IX 1 T 1 .33 I 1. T .4 D a» I
I S 02 . K T I 1.2 2 c K I I E T
I I S I T .. I T I O T T .. a ..L R ....
I C I9. 1. R I 2 L2 I 1. P 1 H O I
1 E H I . T 1 1. H I . T F I F C
I 1. R 59. T K I H 09. .. T K 1 E
I I: 0 .El H T E I E1. nu H T «A D r. R
I I F 1F U H G O 1F E U H 2 O G 0
I I I T O N 0 I In T O R N D 9 I. I F
S I 1 .LI . T R nu TX I . T. I .K R I
E r. X 1:4 J S E 1. (2 U .u S E r. 1
G G 9 I 0 1| 0 V O I O 0 l. I .. P V X
I I I H). I. T I I "2 5 1| T S I 6
R R L S I 1| T L L D I I. T l— T T O
E r. I .Lz I .1 I .b I .r2 L 11 9 I c. N no I
V V U 01. T S T N U 91. I T s T I I N D
I I T TF 2 S 1. 1. T TF U T S .... C 11 I TT
c T. T I I 1| v c T. T D 9. I l. E R v E If.
0 no I .TI 1 I I fly I .1! 1. I I I R .U n. fl .|(
N “N I I9. r. T H I" I.. I9. c. I 1. H O .r I" I .lA
I 1. 1 I"! V I. S 1I In. r..L T c. F TM
2 V V X 52 I T E .... I O 02 R V T E T E 5 ID
I 0 Au 4 1. 1 .1 I L I; to I a. I F c..L n. TR
To In H 1 1:0 T . R .b 10 .10 F. I . R 0 .I n. 0 .00
IT I I T1 T 1 MD 0 U IS 11 OTT H0 0 C U T (F
I... I E D ‘F 1. . UT I 0 D . 11F 1.1. UT I H E 0 R 8 T
S... I L 0 T. T .6 T NS 0 TT I 0 0L TO 3 H.. NS 0 U R 0 E MT
ES I P I 1! ITTT H C! T I! H I II OX 1 UTH ‘9 T S 0 I P .1
Tr. O H R" T3 .TTCYII: U .IL.JIJS .TCCPé. 1 RU.1§..§ SH“. .R 1. 5 RI .r I I T(
FT X I E To TIOGUQZN JI 0 1. TOOTR I ED T1 QQIUN JI 0 J1 TO I I 1 J1
. E 3 S P .12 J (1.50.535 . TCV I HT JT1|SSKO 5 FT (2 IS ON . TCV I T KI I Q X (T
T: .3 I I T XI TTIIIS . SSJRIT 2 U5 2 TIIITF 5 I S XI 55X . JRIT 2 MG T9 ITSTST IT
IT T1T1T1IJT1 HIHHHIJTTIIOB .DN. OHCHHHQTTOTOEJTO TT9J¢I03 .OU. Q3T901151 HO
‘1 OIZXSXOOIX 2UCSSSH‘54CVIO (TzT 2UIDDDO9910XROOX 503((VID 1.INT O1236I311 :5

TI. 2Hn.° 2a I 221. ONIEEESTZB . ‘13 Is It INHEEF‘.51.H32I 2‘9 23 T1|.1|1.3 I2..T. 3’ I I‘d/...I: T5
..QE '1. 1:.1140..0QE1..M 9 o o OI 1 1...T.| 9 DII‘EI..00 o 9 10 91 13 1:13.». 1 OIIQTT 1 DIT‘E Ola-I OI CI... 1. O
TSU61|61|6ISTGTUMISGQZ-J9665R ..GOTO IUHIFSIS666‘GTIISCU66‘35R .. GOTD IU61|11|61161| ITS
ISNTTITTT 1..TNU 01.1.531I(50II IS IIHNU OISSITCTI‘TS CTNC‘TISOIC IST9HNCTFTTTCT3..IC
(ETEIEICILSEIIN33SSSSSEE‘SHEO..GLAJSINQTQSSSE—LEIEI 09—..ITEEIS‘SHEO ..SB SIEI TIEIEIT.THE
STTTHTHTHI9THT :15 .. .. : : ..TT .. : ST .. M .. SET ..QS: ._ ..TTTHTHI TTHTTTH : .. ...UT .. H : BETTPXNTFTMSIUT
....LNIQID‘TRU Ta‘NH ..5‘23...ITR9...TR33 .INH ..BQSTTRIRL IRVTIQERDEIQDD (“1.12.11.51.19 (3.1.
T ORORORODOROOUO3IISSVRRITSRTTTOFOUOQISSRRROROIOROORROVITSRTTTOFOROOOROPOOIOR
E C HFHF HFIDUFCNDSSSSSIUHVSH HKSSDICNDSSSSUUUFUF UDUFCHUFIVSHUKSSDICUFI FHFHFDTFH
I

1 1

1 9 p. 1
8 a. 2 3 48 3 C 9 9 O 99 Q 3 5 9 6 3
4 2 2 2 29 1. 3 Q 3 3 Q7 3 1. 5. 5 .... 5

.3

31C
1
320
325
33C
335
310
315
350
355
360
365
37“
375
380
8

1.

E39

FTN IIB’SEI

PHDHP

=1

09?

141175

PROGRAM DELUX

EXPONENTIAL SHOOTHING'II)
D'ISXI'ICTUIL'ISXI'SES'I9II'FORECAST'I6XI'RESIDUA

SIXI'OOOEXPONENTIIL SHOOTHING‘Ofi'IIIT
O'IIT

SXI'SXNGLE

ESSOI!)

ES
F1

2.2.2‘.F1.02T

x

I

T ITIJT IJT I
617 OBIS O9X
2H2, 9.5.5129

E 7
a.» A.

573

393

B
a...

395

9‘
55¢.

T TSIT9
TITYISOTIS
TTIYII OSI .651

2T
1.!

.OF 1‘ I2T

UH 0F RESIDUAL SOUIRED=

)

)-1IIAVEI-2)

ITOIOTSOSSI . 3
TTTTIISOSIESSS OT . TV

l(¢(J-3)-1)-1.O)I

BEEEEEEESESIJFIJI. OI . I3
5 O1 OI 35R: 15.....SDTSI I I I IEII I IIléT O
UEISISII 19°C.UTFFFE01678T5966IISR6
HITITIT 0 ‘..TM...‘

KTRII

GTISTDIORIEDESIITILTISTDHTKTR

T
n

O
2

OIIJ-ZTTOISS6T

J

I
I51:T

TD
3
)

To:

SQXI'DOUBLE EXPONENTTIL SHOOTHING'IIT

DES“ 13XI'EI'912XI'E8'IIIXI'FOR

'.
Lisa-.1;

7
I

OU

I
0

IT.

ITT 9T 9 OJ, OT
C9Q16XX O8X2
3....7H787179 I
DI (TIE O O O1. O1 O: 91‘... OI

81C
IUH OF FORECASTS: 'IFIZIZISXI'SUH OF RESIDUILS= 'IFl

GI
ea 0
TI
09
93
3 O

SUGSGIEII TGIIUSI

O O I IIISSSESSIIT9SGI IS ISOENIIITITT ITFNIT

IEIEICIXIEITBESPO.$$$SS: :SCFISISEAJ:2EEDTEEEIEISTEI OTEI

TTMTVTH:.1THT3S$S$::.... :23:TTH: :..T:H:SSETTTTHTHITTPXTTHTT:= :T:M:hE.LTTTPTr..IFTTM.T

”IRI‘IR 0 1.1V

09: CROROI 09000568911555555RROVITRTTTSOFORRROROEORO TORO IR VITRTTTSOFORROPOTEPPOR

CUFHFUFLDUFCDSSSSSSSSSSSSUUFIVSHKSSHDICUHUFUFRDUF
I I

: : : .. 01.570.11.31 .TR...9 31.103...

Q00

405

410

391

Q15

923

C
8
E

425

q
7

6
7

430

a
7

“IT-IVEOOZTIII(J-3T'1T-1.0T

P
-1)
)

ST...-
.3... . TV

KTRol

GTISTDIORIEDESIITILTOSTDHTKTR

T
a
S
S
I
I
T
T
2
T .
0 J
I I
2 IJ
.DOOI
IT IIDT
I51.:T.

OXI'OOUbLC EIPONENTIIL SHOOTHI~6 FORECASTS“)

DIIIIEII/ 91..

To .-

SQII'TRIPLE EXPONENTIAL SHOOTHING'I)

EDT OT
...:1112
T51.H3
T. O OT O

SU66(6 I(6b(6

I13 OI IS ISTENIITI? .. RIITI
ESTSEG: 2EBUIEFIF3T0§FLE

INITIRTQC TRZNIRZI..5\DIR)O.L

INTI-1.11.

(STIR x

2CUF2UIVSHKSSNDICUHFHDTAJUUF U

Q35

7
1‘

390

no

aas

453

987

D.
5
5

I69

90

FTN IIBOSbI

PHDHP

=1

OPT

TQIITS

DELUI

FROGRLM

C S I I I
T C 9. I I
I T 1. I I
O E F I I
X O O I I
1. T X I I
1 I 3 I I
O I O I I
I S 2 I I
R E I I I
T T 2 T I I
I E 1. I I I
O O F s I I
X T O T I I
1 1. X S I I
1. I 1. I I I
O S O c I I
I T E 2 E O I
II T I R I I
T O F 2 O I I
I I O 1. 1. F 2 I I
O0 T F O I I I
XS I O R G I I I
C. I X T T N T I I
1.L C 1. a K ... 1. I I
OI T O I 3 H I I I
I U O 2 1. R T 1 I I 1.
50 T I c T o T I I
[I z 2 T K o I I I 0
TS I 1. 1. T H 0 I I 1.0
IL 9 F . H S I I I 1
OR T O T D 2 I I DR
II O N 3 T L I I I OF.
9 O T 1 o S I T I I TF
OI I O J I I J I I R
I 5 I 2 I T T I I I ER
L O I I I L N c I I Po
II T 2 I I E T I I F
UL O 1. I T N I. I I N
TI T F T 1. 0 TT I I TC
CU 1. O 2 I P 1.1. I I 0
I0 I x I T s I II I I [I
IT 5 2 I 2 C E TR I I OH
OS C O C 1 T TO I I I
XE T 2 V S .... F. IF I I "T
IR O I I S I L T5 I I S
OI T UT I I R P JE I I TI
I O 1. 12 T D I 0 1. IT I I SCT
DI I F. 1 I T T I R BO I I ACT
06 T OI 1. T o S T D T TT I I CRI
TO O X1 $21T O 2 T I Q! I I {op
RI T 3F O1. . 3 R T . S R O TI I I FFF
ET I OO EST. I O J I T I J1 IDI 0 F
PS I 2X c.53JTV O I T K 0. IT I0. FC-
I I X 1.2 TTcIRT 2 IJG TTSTT IT IHI HT
OICJT O O OTJII‘. . on O I I.) O1. O To I TI [TI
IL O3 X2 99I . V0 IT I3T 05/31. :5 IE. H I
3R1...) 9 I 1.3I2I3 .5121 3.3/5: T5 I" I TST
1C:O TZEOOITTO DIITIEOOIOI TO I I T
IFIS (1U6615R6 T0: $U6£I6 1.I6 ISI 5 5
TI I TFNIIISOI Is ISI.CNIITI3 ..RI IR I IT:
I OTCTI TEESISCO:2CCTTCFIC3T 0C ICI 1.
MX9T1.HITTT:::T:M:T9ETTTHT51.FT ITI TIT
R5 EIRZNITERDIRJDE INIIRI (51 IN. IF]
0OOROUOORRVITRTTTSOFORROROIER III IFI
FI DUSFZCNHIVSHKSSH.DICIUFNDTTU IUI FFR
I I I
C 3 3
2 3 7 .J 5 3
.3 3 9 9 5 5CCCCCCCCCC
E. pl -\ nu I U K. c
6 T 7 8 8 9 9 0
I I I I I I. I 5

0 1. 0
C F L T
O I
L I N D
I 0 N
N .o s o
0 I I F
S I E S
I X S C
C 1. R
S O o R
T 3 N 0
D I T. I c
N O O
I 2 I D R
I T N C
D 2 I D C 1.
N 1. O 0 R H
E F 2 T. T U
R O I R
T I 2 F. O I
1. P TT T
O : F NI I
T T T O R 5 o
I N N I o N O
I E E F II F
I N N : RI 0
I I 0 T R RT
O H P N 0 CI 5
I R M. .L T PD 0
I C O N C O
I P C O I CC 1.
I P F NH RT
0 E T H TT CI
0 N N O L F O
H T r. C I FR I I
T N N 00 O3
F. F I D 0 R XE
H O H N 5 SF 15
R C I F. OU
S S C R E U0 3
R E F T 5 LC 1.:
E U IT O8
T LT L L L VI I
N II I I I H L
1. U, 1. 1. 1. L1. TL
H O T T T IT 51
I1. LI 1. 1. 1. 1.5 RU
I8 IO N N N T... 1.
I IE 1. T. T1. 1. Fs
I 0 T1. I I 1.- NL K N
OT IF O O I O 1.8 Kalo
X N1. X X SX I OHS T
T I0 TC 0000 OC O0 1.TI 2J
T. TSGTI ENTIZBZUTZ XT NI F— R JIL
NO 5 OTo OFLTT OT OLT O T. T OS K OTR
OI ITTSXS OIIJQIO O60 71.5 EXI O 19’ 1.
1T SHISI TSEHBHIBH 8(T POO 1 JTT .
: IC O10 O15: : O1. O1... O1 6 OTNH O1.X ..ru..1.1. HF.
IDUSICGITITGISITSI 96IEL6I1 TIJIIILU
UNIT IITN IITIT ITT IMNIIT O 1 O VVI IN

9 ..IEINCIFZIEICISFIIOEROTEISH H9 :0. = : 21.1.

9TTTMKTHN€CTMTMPTM TTOPNTPIL1L0.T9TTJJT

TNTRIIRO VTRIR IRI TC..:1.RO::: Y. 1.1...:N

OTOROFROPOIROROOROIOR OKROILIZOIOIIIFO

DTCUFIUFHDSUFUFDUFUGU CKUF RJJDVDVVJJC
I I I I

9
9

SOS
350

23
PE

PI
5
6
1
7
B
0

9
I.

505
510
515
520
525
530
535

91

FTN QIUOS£O

FPDHP

=1

OPT

74/175

PhLGFAP DELUI

SXI'SHOOTHING CONSTANT OPTIMIZATION ROUTINE'OIIT
ILPHI.O1°xO.eETI'O1UXO'GIMHI'O10II'RESIDUIL SUM OF SOU

YIJT)/IVIIT-IIIRL’IIOTIZIOT-RJTOPOT

: :I = [0 J :IMN OO:J: O0 91O3T
1J1 T1UI OIHUUSSJIT6C6I6I/
J JINOKOI USSII SJIIITITO
...VI 236 O11...KIOIS::EEI...IESEI.III
h...V..99JJIJTS:I:9..TSTT9)ETKTHTHS
.. : .. : : :I:VI K I. HJI 1:... JVTIIRTD‘...
R001OOTJF1OUKOUOUIURROIIRFROROR
R8IJDDJRFJCSRDSDSSSHUDSSUIHFUFI
I

c
T c
R s 1
R H T
’0 U JO
Thu T 5 IT
TI J T I 5
1I H O J00 L OD
I2 K” L KIKIIBHRTJGTRTI
VI KL O KIRSTTLIJTT1O2O
.L OOH 1 OFRISQOIISOOIOX
TP 11L : 1F/5881T55I1H1:
HR.
LKT
. I1

0 I 2

3 .2 I. Q .35 0 c

9 9 9 1 99 1 1
I 5 O. s a 5 o
I I 5 .3 .b 6 1
5 5 S 5 5 5 5

SEARCH FOR" OPTIMUM VALUES

C

T
)
1
o T
1 2
I I
B 5
RT 1
I1 E
T. O
III. In
T .I E
0 I18 O
B IUT 2
I IIL I
0 T H81 2
I OI IrDI 1.
IOIT INS T 'I
IHST IEI T O
IIIL ING L X
I850 "06 L 2
NPG1 [0” H1 O
EMHI NTE LI U2
HEES OTN .5 [IS
ONNI I10 TIZOZO
IOOT T.I LTIGll
TIIT TIT LTIGF
TTT12 LIT 11TOOO
1OTII 1‘1 ..ITUXT
II18I IHI THIbS
OnXu S..IU|. c..A .LUPIUOO
III ’TIIT HIT“ LIROfl‘G
111 T1UTI LTT/ TT.HIT
III I“ BU GUT 1I’LH =1IT TLTIZT
DOD EKI Kb KLLGIITXX1 LII1 HITITS
I86 BOA O8 OITGYH10.NT1YUI LILTFE
I], I1. 1. 11I.IIIT)OUTII' ITIOOe
TTT [:0 :0 ==EOIIY1T2L0IIITTTT1XCI DD

LLL ODOCII JI KLVIIHIIL:OIHUILGIIZZIIHG HA
IRG IIII11 T1 TTIIABIAIIIOAHOIIIYozileHDII
. . . 0001 : : S:IBGB1. (CIBGLTHIéIG:B:EG HH
UUUL: .. .. ..SILOB 56: G: : GIITD I: : ......LI I IT II : I : I BI
IBGITTTTBIBCBLFOTSTT::YOOLTT):L:HEAUHAHTGBA
III:SSSS1Hz1HG11LH11TTI1H111LT1TETHEDTMc5::
:::JEEEE £4 E: TEIIIA: :(IITLTI:I?(LEAE:JI
AHGABBBBONBONGOOINABIHHOLFAEILFHHRUFABGBbBA
KKKIIBGEDOBDOGOOSOUHSIEDTIHHSTIIEUFIHUHEGBA

10

‘2‘}
Q .A..Al~

6 8
o c
1 1 lTol

137

575
583
585
590
595
60C
0
blu
615

92

FTN ‘06’56Q

PMDMP

=1

OPT

TQIITS

PROGRAN DELUX

'!F120295XO'GANHA= '9F12.2)

N6 CDNSYANTS ARE SPECIFIED AS3'QI)

HUM SHOOYHING COVSTANTS ‘RE:'Q’,

UFIFUFI

.‘fdr‘ 3
lord... 1
‘oll 'o

62

FORECAST HIT" OPTIHUH SHOOTHING CONSTANYS

625

,
’
1
.
I
‘
a
U
0’
)1;
1.
) .1
o .11)
B (BL
I 1 ANY;
0 1 HI-
R 1‘ ‘Bs
1 (a OBI
IOI RHG
R85 REG
A .5, MN" ‘0
HEM... [0... T
[PEI NON L
NHNT 010 L
OEOL I). H1
ONO- ’1’ LI.
.1015 1 .1 . S
)I)I L11 .II
111) 1“ L)
(0‘) (AA L) 2
5AA... ‘1 SH” 11 ) I
/.U‘ 1 l.’ :l‘ 1 1I
’iila ‘ .l": Thu ‘ I!)
I ‘11)” F 1195 Lu- F 11
HINT-3.1. . H‘C‘ LI . In;
FTHYACT ) LYAY 1T 1 RR
HirLEAl-HYL \: T 2) :‘U‘ ’L)?! ‘9
LLABGII‘I‘N 1 L I)... LI‘I ”NIL so...
1UHUII I I I. I I1N11AIA LICI)BSL
1C . . . HAI’ F 1 1.! 0U1HAH) I1F11IH O
..LOOOPTH1I... C 1R2LOPTPLTTI:_I(IU1
LVoooLEHC1) Y ((:OoLEAILGl)YRDS: o 0
IA111AHARCT ..‘IRSIIOABG‘Q OAT... 0‘51 5 0 o
S: .. :HUGUSL 011:8 (EHHHSLTHL1HM .. o: .0
5.. ‘85.. ..H‘: 90.!10‘60 0.. = .. ..1L‘ITUX080)1°:

11APG),::11:LRS:1.OL)))):L=ILS:51:19 :2

1LHHH11)’1() I : u. 01H111L1711l I : 0H1111—LE

1r...:..((11.|P11qUR : (((1(L(IPII RU 1? NH H

O(NNNABCCSF((USHOLFAH(SLFCFCUMSO(F:UU

DSOOOHUSFSFRRSUXDXIHUSSIIFFRSIUDRFJSS
.

5 7 6 8
1 1 1 1
1 1 1 1
0 5 U 5 0 5 0
3 3 R Q 5 5 6
6 6 6 6 6 6 6

START THE FORECASTING PHASE

665

O, 2 F
I, 1 9
'l O t I
NI 0
[L X :
NA 5 L
DU 9 A
D D 2 U
M1 I 0
DC. 2 1
CE 1 S
\a R F E
I .II 0 R
I V I I
'.LI 7 E
I N9 I. G
1 E R O 2 A
I- S ”I I P
1 an RL ’2 E
. H EC 11 V
I P PO ‘3. A
..I I 0 R Q I
B N I" 0x I
H 0 I ,7 X
I, I 90 1 O ,6
)1. 1 IL (09 I
I... N I 9' P O .2.
.1 7. Nvl F2 I
1‘) 1 01 F1 2
‘.8:- L IF 0.? 1
)‘HI ‘ TI \1 O F
LuIl‘ I ‘ 0 1x O
1‘85 II VI CQ I
‘IBI 1 R“ s 9 1
SANG N E 0 52 c :
IAEG 1 SI 0 I I S
)HNH BR )2 1 L
’50.... E C0 11 . A
.ININ H I 'l (r- T U
L010 T 9C B I H D
- 0’. NA ”x 1| 1
1,11 F 5...: 91. I S
'1 o I! o 9 ’1 \I E
8L1... I L I O 2 R
HICC T 0‘ (2 I
I‘ll U 0N R I I F
TSHU P 10 H2 ..L r20
Ll . I 2 9| RS 91 V V
X1), I U ER 1.? A An.
0111 I 0 Fr... 1 I. U HU
“H"!l‘ \l ‘1 I I s ‘N I 95
LT'RY I I 9 OI '5 T) MI
:LI‘HI. I." X X. 0. UR U.
U L.I(I P18 0 0x113 .A S!
N111! IA Fl. o)5)17N)1 OVT)9

OH)(H|H)FR220390050 TSUU63
JLCAPTHL.¢E2120-1ZI “MC/29
: O IULEAI’EH1H1HD:1E IUT01/
IIECABGIIHU9191N101 MSRAOI
1L:HUUS‘U56‘6(E 6‘ UHOH b-
00 I): : : : VS : ‘T(TRQ(II S‘SX‘Y
20L1))))::2EAEAT2EA 1::::£A
IHICIILI)ESTMTH-1TH NCPDDYM
_. (D ((I‘Ilv "1‘1; 9 13": ““T‘Ia
OLFFAB(S(UUROROXOR02TAVSH90
DIIFHHSSRSSHFHFéDIFoHHHHIhF

I I
1 «J 2 3 ‘5 F
2 2 2 2 22 s
1 1 1A 1 11A 1

610
675
683
685
:9"

93

FT" .IB‘SE.

PPDFP

=1

OPT

74/175

PROGPAM DLLUX

S I 5 S
I I 1 I
C X S C
r. 6 E
R I G R
O I N 0
F, T 1 F
I N K
I F. C E
I N A 6
5 O R I
I P T R
I H I E
c. 0 I V
D C I I
0 1 T 1 I
1. T 2 ca 2 I
1 1 R N I I I x
I I r. E 2 I 2 5 1
I I P. N .1 R 1 I I
2 .I I I r. 0 1 F 2 n
I I I H I R I I I O
2 I I I” I R I I 2 H
1 F. 1 .L T E I T 1 T
F 1 cu I P I I R I F E
I I I 1. I 9. I 0 2 I H
I R H 1 I I X R I I
T P I X 2 8 R 2 S 1
: K I 9 .1 1. E 1 : P T
N : 5 : I I I F S E .
D R N 1 I I.I I h. I R T I
I T 1 5’ N 1! T E I D N I
T K T 151 0 (5 c. H 5 R I U
I 1 S I 1 (II I .I cuI R N N
1 H I NI T 52 C 0 T2 1 E I
V D C 05 I I I F. O N I o G S
E T P. SD '1 12 R N I2 I T N S
D S .K I0 n3: 1;; O Q. C1. .5 S 1 I
U 0 r?;.LI Ir..r I TF . I S 1
E o r..2K S- D nu! I o D “I. N a» U )
T T .L BR A “IX .I I A II In E H
U L F EP 00 N I1 I e H 11 I! R 1 s N
L I 0 HI I7. I s:1 8 I I 131 .I 0 0 T. ‘1
O 1 T I IC I T. I I I I I. I 1 F. 1 s 81
S T. T I II 9 I2 I R 9 R2 2 s I H1
D B C U F1 5F I I. D O I I. I 5F 0 S C c?
T A R P.nuI I .9 H2 nu R o ‘5‘ I '0 T. C r. 1F
5 I T 3 I L I I1 1 R I 11 ... I s I R 1.?
U N R U H1 DI Z1 1.? R E Z1 If v N” N 1 1 o a! I
I I 1 O OTT I 0“ U1 1 I E “1 P I I IU1 I 1 1 F 11
.PnFL 0 I I.LGI .10 IT. (in P I .1. .PX H r§§2R 1 .2 a‘ 1 I T1.
AAM o D I" II" Rh. 91 III I N 9( :30 01MB 25 1 I .u N o. 0‘
VMI 2 1T T INF—s .LI IR I I I U IR I I NRU 2' I1 I s o X 11
“X I . CNS K CLLT. PE H 0‘ 13 I c N at. 1‘. XISX1N "9.11 “IN N 5 C NT
11! (TIN 1151I 1IS N IS 1115 1I N IS 11 N.V19F1 NFCI NF N15) IT N11
.219 0:71. I0.{.ll2oi I 1nfiK35991..30, I 1Bnfi¥aI I297i915 IFPI. 2L IQ.i.nuI_¢09
023 ON T 0313XH3X I J11III3X5 I 3X J11III5X IEC3 II 0 1 2 J . FR JO 1.5/30 :1 ISI
31 I T I : G 31H16115X ..IaII ""1611, 10 =11 I ""15 EHT1I 3 o 2 . 3:1... .. :0 One/.... I1: “I50.
I II Sn...‘ IF. I 1 1T 19 1(R1II I1 I, I? 1‘R1XI I11MUR II: I HUTNPIII 12:11.}. I II 5T1 I I I
66( Ho 1U56¢6C 6(0 Raul/6(6I 6( RIo/ISCNUSGé‘RélLLLLL IZIU SU16(6:. 1:66
ICT :281N((T‘TU(TI0°.I10TZCT¢T1CT002I10TZIT.SIS‘TO‘IIIIIIOT1IN1SNI‘TI115:1((
1EEI0M : 2115?.IEIIEID I ISV. I: WHEIEII [I I IST I :UHEIH: .. ..EIR—LN21315 :5015:1:EIE1¢511EE
2TTM..DOIPTTTMTFETHNCDIHDD:..TNTHSTNCG1HCD: ..THNGPDTHRTL..: .... ..11..$Tq.r.THTHT (H¢.I(TT
01.1RRTT (‘11.! 1.11.1.1... : : : .. A. .51: In. LIR : : : .. A351? : VAT..52L1 : 121.35 IZIV INEID 1.: N (D 1.1

«SHROTéibOCAYhRCRn..KORY5EV-ZMTéJKORdifu0Y5§UTZMT§A§UNAUEERU RUPTBCIPOIififOO:X§2HORF}1U1FPRP
.JHHrLRIIDI:EIHFUBEKHFTL!HDUH:3IHUKLEPNHELEUDUH33IHIFLEIUHHEBLILIF???LDR¢§ECDQF§TUFHFnglrUH
I I I I I

T In a 1. 2 5 .Q6 Iv 3 21. T o .1 I 5
2 2 tucé I. 3 33 £4 3 Rad 3 5 la 5 5
1. 1 1 1 1 1 11 1 1 11 1 1 1 5 c .

695
700
7C5
710
715
729
725
739
735
TIC
745
750
755
760
76‘
770

94

FTN “I595EQ

PHDHP

=1

OFT

74/175

PF CGF AP DELUX

D
.U
H
T
E
R
G
N
I
T
S
I
1 1 1 C
$— 2 2 E
I I I R
I I I 0
1 I. 1 F
1 F ..r F
I 1 1 I I I T
R 2 2 In K I S
C I I I. Q I r.
R 1 I. I I I I a
R 3. 1 1 I I I

L I F .I G G G E
I I I N N N H
—.. 1 x X I III III 1 T

R F 1 1 H H H 2
I I 1 1 T T T I I
U X I I 0 0 O I. S
C ... I I O C O 1 R
S 1 E E H H H ..r E
I G G s S S I T
1 M» I I I X f.
I I N R R l. L I. 8 H
S r. o E r. I I I 1 I
1 H 1 V V 1 1 1 I R
C. I s ‘ I T T T I A
T I S N N N D P

L I r. G G r. .... f. 0
I I. R N N N N N H N
N 1 G 1 1 O 0 O T ..L
I I r. V V P P P E V
I R o o I I I H 1
D D H H E E E G

0 0 E S
.H H .L E r..t E r..K G
T In P .L L .L L I..L N
E E HAPIBSGSBSR T 1
M. H 1HMRUF.NEUE1 N S
I IPSSIDCS150TRH1 U
I It; ESEnJC.anhLET—Lnl I
x XeeISISI SI SI SI SI I
1 INXNIM IRIHIHIHI X

1...].3 13R:.I.345Q5Q54r4 I
H9/9/9 I9 I9 I9 I9 I9 I61
1 I, I, I, I, I, I, I’ I, I,
I6I6I6I6I6I6I6I6I6I

9 .. 1 ... 3 I 5 6 7 .J
I I. ... c: 5 5 5 ... .3 5
c a. 9 9 9 O. u; 9 9 .t

C. (L f.

T b e

T 7 7

793

5935 n 35 35 5 63... 75 8 15 2 I
0111 111 11 1 011 01 I. 11 1
06666116650266036OIO 666055°6n666c60760890
1:1 p0 0f. AU K. .‘ . 1. 0. .fi. .JGEALF.
600006.9000660°6606665000600606600606606F.66
TTTT TTT TT T 2TTT TT T TT T T
0 00 00 00 0006 0 0 00 0 00 0000
TOOOOTTOOOTTOOTTOTTT OOOTOOTOTTCOTOTTOTTTT
5556 555 55 G 0556 56 5 GB 5 G
01111 U01110011001000T11101101.U011010010000
GISSSGGSSSGGSSGGSBGG SSSGSSGSGGSSGSGGSGGGG
1NEEE11EEE11EE11E111OEEE1EE1E11EE1E11E1111
IDSDTUISDTHSOTHSTLSHGSDTHDTUTUUDTUTUNTHNU"
REEEEERLELEEEEELEEEL1EEEEEEEEEEEEEEEEEEESE
SSCLC.SSDSI.SSCISSSDCISTC.HCISQ.IIC.SSc.cu$c.ss.bssssscus
EHHHHHEHHHHEHHHEHHEHEHHHHMHMHHHHHHHHHHHHH"
SIIIIISIIIIQLIIISIISICUIIIIIIIIIIIIIIIIIIIII

9'0! U1NTERS METHOD "'1

HTTTTTRTTTTHTTTMTTHTHTTTTTTTTTTTTTTTTTTTTT1X 1X
ILLLLL ILLLL ILLL ILL Il. ILLLLLLLLLLLLLLLLLLLLLIIO 13
TIIIIITIIIITIIITIITITIIIIIIIIIIIIIIIIIIIIIIu‘. .35
LIISSSLISSSLSSSLSSLSLISSSISSASIISSISISSSSSB I86 I85. I86 I36 I8
IMMErF. IHEEE IECC ICE or. IM_._EEM...FMEMHEEPEHEEEEE II... II... II... II... II...
RSDSDTRDSDTRSDTRDTRTRSSDTSDTSTSDDTDTDSTSDT6I6EI66I66I66I6
TITITITITITITITITIT1EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEPLEEEEEEEEEEEIT IT IT IT IT

IEAr.IEIEIEIEIEI—LAEII SSSSC.SSSSSC¢SSSSSc.c..$$$<.<.sssss(ISSSSSSCVSSSSSSEAOEIOEIOEIOEIO
MTPTHTMTHTMTMTMTHTW..MPMMM MHMMIHHI PMHHFHMMPMHRMRMHMVHNNMNPPMMMMTPTTMTTFTTM TTHT
R13.IRIRTRIRTRIRIRTRSIIIIIIIII. IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIR IR 13. 13‘ 13‘

OFOROROROROROROROROIFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFRODROORUOROOROO
F HF HF IFUF IF HF IF HF IF 111111111111111111111111111111.11111111111UFGUFGUFGHFGUF G

0 1 2 1. I... .t 7 an. 1 23 I...
2 0 0 0 fish. 0 a 51 1 11 11
6 6 6 b 66 .t E 6‘. 6 66 6:.
K. II .5. o .3 0 cw. p.
9 0 0 1 1 2 2 3
T H. 8 8 8 8 8 8

1 97
... CR.
..c 66

to

0". TRIPLE EXPONENTIAL SHOUTHING II.)

I... SIMPLE REGRESSIDN 00‘)

1X
28
55

‘7‘ bi.
25 2..
66 .LE
.U
I.
.5

1R
36
5::

I... SIMPLE MOVING AVERAGES 00')

be"' DOUBLE MOVING IVERAGES 'I'1

I1

5
5

T“
«be

EIS

I"‘ DOUBLE EXPDNENTIAL SROOTHING 0")

I"' SINGLE EXPONENTIIL SHOOTHING I0'1
1
III'THIS IS THE LAST PAGE SO THROI 1T ABAV'1

1‘ 1x

6 I66 IE9H
DIE. III. .1
6|66I66I
IT IT IT
[ACEIOEI

Tu: TTM, TTM-P
To“ 1" 1‘7.

3

RCOROOROTN
HFGUFGUFSE

I... 96 BI
E‘. LEE 109

USC
855

llllll\\|H\\|\||lH|lNIH"H

1293 03085 4

N||I|||
U“
E“
Tllll
A“
I"
I“
H
ll'lll

594

3