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MULTISTEP PREDICTION IN AUTOREGRESSIVE PROCESSES

Published online by Cambridge University Press:  31 January 2003

CHING-KANG ING
CHING-KANG ING
Affiliation:
National Taipei University
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Abstract

In this paper, two competing types of multistep predictors, i.e., plug-in and direct predictors, are considered in autoregressive (AR) processes. When a working model AR(k) is used for the h-step prediction with h > 1, the plug-in predictor is obtained from repeatedly using the fitted (by least squares) AR(k) model with an unknown future value replaced by their own forecasts, and the direct predictor is obtained by estimating the h-step prediction model's coefficients directly by linear least squares. Under rather mild conditions, asymptotic expressions for the mean-squared prediction errors (MSPEs) of these two predictors are obtained in stationary cases. In addition, we also extend these results to models with deterministic time trends. Based on these expressions, performances of the plug-in and direct predictors are compared. Finally, two examples are given to illustrate that some stationary case results on these MSPEs can not be generalized to the nonstationary case.The author is deeply grateful to the co-editor Pentti Saikkonen and two referees for their helpful suggestions and comments on a previous version of this paper.

Type
Research Article
Information
Econometric Theory , Volume 19 , Issue 2 , April 2003 , pp. 254 - 279
Copyright
© 2003 Cambridge University Press

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