This dissertation considers methodological issues involving both prediction and model selection in the application of long memory processes to economic time series data. We also have a section which discusses some practical aspects of the implementation of the model selection methodology to real GNP, monthly CPI inflation series, interest rates and realized volatility from currency markets.Chapter 1 is the Introduction and sets the scene, established notation for the approaches to be used later. Chapter 2 examines different approaches to estimate the optimal, minimum mean square errors (MSE) multi step predictor to univariate fractionally autoregressive moving average (ARFIMA) models. We consider two competing approaches of (i) using the MLE of the ARFIMA parameters inserted into the optimal predictor, and (ii) using an alternative predictor using estimates arising from the Local Whittle Two Step Estimator (LWTSE) are applied. In the latter approach, an initial semi parametric estimate of the long memory parameter is used to feasibly fractionally filter the series to obtain an estimate of the short memory series, which is then used to estimate the short memory ARMA parameters. This latter approach seems very relevant given that the most popular methodology in current econometric literature is to obtain an initial semi parametric estimate of a long memory parameter. We found that the predictor based on MLE is generally superior in MSE sense to the predictor based on the LWTSE estimation. In general the <&ldquo>optimal bandwidth LWTSE brings about worse predictions than the LWTSE based on the conventional one of using an agnostic bandwidth of the square root of the sample size.Chapter 3 is concerned with the issue of model selection and considers the choice of lag length of the p and q parameters in an ARFIMA(p,d,q) model. Perhaps surprisingly, there appears to be a major gap in the previous literature, which has only considered this problem for the very restrictive case of the ARFIMA(p,d,0) model. We show that when estimation is performed by either MLE or QMLE the AIC is inconsistent and show that the widely used BIC and HQIC are consistent model selection procedures. We accordingly extend the theory to be applied to the ARFIMA(p,d,q) model. The implementation of the technique involves selection of the maximum orders of the short memory process that the investigator is willing to consider. In our simulation study we restrict the maximum values of p and q to be 8, which involves 81 different ARFIMA models to be estimated by MLE and then assessed from a model selection perspective. In our detailed simulation we consider data generating processes up to orders of an ARFIMA(4,d,1) model. The BIC works well for some low order models; but has a mixed performance on high order models with p = 4 and is quite dependent on the part of the true parameter space. We also show how the theory can be extended for seasonal ARFIMA models.Chapter 3 also considers the two step procedure, which in this context amounts to the application of the LWTSE where an initial estimate of the long memory is obtained by Local Whittle and is then used to fractionally filter the series. The short memory ARMA(p,q) model is then estimated by the minimization of the conditional sum of squares (CSS), which has been shown by Robinson (2006) and Granger and Newbold (1996) among others to be a valid procedure. Our simulations show that this procedure can also work quite well, but generally not as well as the previously discussed direct estimation of ARFIMA by MLE.However, the above procedure arguably suffers from the <&ldquo>generated regressor problem and following recent work on factor models in VARs, it seems possibly desirable to also include a small sample adjustment to the BIC which reflects the sub optimal rate of convergence of the Local Whittle estimate to the true value of the long memory parameter. We also report some simulations to assess the effectiveness of this procedure. There are some cases when this appears to be a useful procedure.Chapter 4 provides a detailed set of applications of the model selection with MLE and LWTSE to real economic and financial time series.
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