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On prediction errors in regression models with nonstationary regressors
Book chapter

On prediction errors in regression models with nonstationary regressors

Ching-Kang Ing and Chor-Yiu Sin
Institute of Mathematical Statistics Lecture Notes - Monograph Series Institute of Mathematical Statistics Lecture Notes - Monograph Series, Vol.52, pp.60-71
2006
DOI: https://doi.org/10.1214/074921706000000950

Abstract

accumulated prediction errors;final prediction error;least squares estimators;random walk models
In this article asymptotic expressions for the final prediction error (FPE) and the accumulated prediction error (APE) of the least squares predictor are obtained in regression models with nonstationary regressors. It is shown that the term of order 1/n1/n in FPE and the term of order lognlog⁡n in APE share the same constant, where nn is the sample size. Since the model includes the random walk model as a special case, these asymptotic expressions extend some of the results in Wei (1987) and Ing (2001). In addition, we also show that while the FPE of the least squares predictor is not affected by the contemporary correlation between the innovations in input and output variables, the mean squared error of the least squares estimate does vary with this correlation

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