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Statistica Sinica 15(2005), 447-476





ASYMPTOTIC SECOND MOMENT PROPERTIES OF

OUT-OF-SAMPLE FORECAST ERRORS OF MISSPECIFIED

REGARIMA MODELS AND THE OPTIMALITY OF GLS


David F. Findley


U.S. Bureau of the Census


Abstract: Under minimal assumptions, it is established that the sample second moments of the errors of out-of-sample (real time) forecasts of possibly incorrect regARIMA models have asymptotic limits with useful frequency domain formulas. Both OLS and GLS estimates of the mean function are considered. With misspecified regressors, under additional assumptions that do not appear to exclude any regressors of interest, the asymptotic formulas are used to show that GLS has minimal asymptotic mean square error for one-step-ahead forecasting relative to OLS and other alternatives.



Key words and phrases: ARIMA, model selection, real-time forecasting.



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