Optimality of GLS for One-Step-Ahead Forecasting with REGARIMA and Related Models when the Regressio
2007/02/06
研討會日期 : 2007-02-06
時間 : 16:00
主講人 : Dr. David F. Findley
地點 : B棟110會議室
演講者簡介 : Dr. David F. Findley為Senior Mathematical Statistician for Time Series Methods, US Census Bureau。
其主要研究領域為Time Series Analysis, 為Seasonal Adjustment與Model Selection方面的國際知名學者,文章發表於Annals of Statistics, Econometric Theory, Journal of Business and Economic Statistics, Journal of Econometrics, Statistica Sinica 等一流期刊。
演講摘要 : We consider the modeling of a time series described by a linear regression component whose regressor sequence satisfies the generalized asymptotic sample second moment stationarity conditions of Grenander (1954). The associated disturbance process is only assumed to have sample second moments that converge with increasing series length, perhaps after a differencing operation. The model’s regression component, which can be stochastic, is taken to be underspecified, due perhaps to simplifications, approximations, or parsimony. Also, the ARMA or ARIMA model used for the disturbances need not be correct. Both Ordinary Least Squares and Generalized Least Squares estimates of the mean function are considered. An optimality property of GLS relative to OLS is obtained for one-step-ahead forecasting. Asymptotic bias characteristics of the regression estimates are shown to distinguish the forecasting performance. The results provide theoretical support for a procedure used by Statistics Netherlands to impute the values of late reporters in some economic surveys.
