Pre-testing and specification search in an autoregressive moving average process with extension to unit root cases
Abstract: Several methods are applied in well defined contexts in the search for an appropriatestatistical model to fit a data set. Preliminary tests of significance for this end aretermed pre-testing. The aim of this study was to investigate some of the consequencesof such pre-testing in a few specific time series processes. The principal results aresimulation-based to allow the accuracy of the analytical derivations to be checked.In simple AutoRegressive Moving Average (ARMA) settings, we illustrate thatthe pre-test estimator is not always dominated by one or other of its components, interms of its bias and mean square error. Further, we found that the degree of sizedistortion, of the test statistic for pre-testing, is generally associated with modelmisspecification. The accuracy of forecasting, after pre-testing, is often seen to followthe behaviour of the underlying "true" process. Moreover we demonstrated that thisprediction accuracy might well depend on some combinations of parameter values,rather than the sole correctness of the estimated model and the forecast horizon. Theseresults are discussed in detail in the first two papers.The study is extended to the Augmented Dickey-Fuller (ADF) regression in thethird and the fourth papers. Here we concentrate on pre-testing for unit root, where weillustrate limitations of an analytical derivation in studying some properties of the pre-test estimator. We also show how the bootstrapping technique can be used to forecastthe Swedish GDP while pre-testing. Through extensive simulations, our analysesreveal that the presence and/or absence of a drift and a time trend in a data generatingprocess has remarkable effects on the behaviour of the subsequent tests for unit root.In the fifth paper, results of an appropriate specification are used to test for theshort memory of a series. A proxy for total OECD demand and Swedish exports areused to demonstrate how the short term forecastability of a series can be extended.
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