# Forecasting, misspecification and unit roots: The case of Ar(1) versus ARMA(1,1)

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## Abstract

~aM~~,ít~ Discussion R for a er8414 -~~c Research 1990 2 i iu NI II IIII'~III I I II II I I IIIII III~ II No. 9002 FORECASTING, MISSPECIFICATION AND UNIT ROOTS: THE CASE OF AR(1) VERSUS ARMA (1,1) R y~ by Jan R. Magnus and Bahram Pesaran January, 1990 zSSN 0924-~815 Forecasting, Misspecification and Unit Roots: the Case of AR(1) Versus ARMA (1,1)~` Jan R. Magnus London School of Economics, and CentER, Tilburg University and Bahram Pesaran Economics Division, Bank of England Version 1: May 1989 Version 2: August 1989 'We are grateful to participanta at seminan in CentER (Tilburg University), the University of California San Diego, and the University of California Ber~eley for constructive commenta. We are particularly grateful to Theo Nijman for pointing out an error in an eazlier veraion of thís paper. Abstract `íisspecification in time-series regressions can have important effecta on least- squares estimates, test statistics and forecasts. [n this paper we analyze these effects (especially the eíiects on forecasts) for finite samples in one of the leading cases where the process that generates the data is ARMA(1,1), but the model used for estimation is AR(1). assumptions about the initial conditions are important too, especially when one of the roots of the characteristic polynomial is near the unit circle. Hence, special attention is given to the near-unit root case. KEY WORDS: ARMA model; misspecification; forecaeting; unit root; initial con- ditions. Contents 1 Introduction 1 2 The model 2 3 AR(1) versus MA(1) 4 4 AR(1) versus ARMA(1,1): the fixed atart-up case 5 5 AR(1) versus ARMA(1,1): the stationary case 9 6 Conclusions 12 Mathematical Appendix 13 References 17 1 1 Introduction Since all models are misspecified, it is important to investigate the effects of misspeci- fication on estimation, testing, and forecasting. In a time-series regression context the true model which generates the observations could be an ARV1A(pt,ql) p

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