Institute of Mathematical Statistics Lecture Notes - Monograph Series

On prediction errors in regression models with nonstationary regressors

Ching-Kang Ing and Chor-Yiu Sin

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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 $1/n$ in FPE and the term of order $\log n$ in APE share the same constant, where $n$ 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.

Chapter information

Hwai-Chung Ho, Ching-Kang Ing, Tze Leung Lai, eds., Time Series and Related Topics: In Memory of Ching-Zong Wei (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 60-71

First available in Project Euclid: 28 November 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60M20
Secondary: 62F12: Asymptotic properties of estimators 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

accumulated prediction errors final prediction error least squares estimators random walk models

Copyright © 2006, Institute of Mathematical Statistics


Ing, Ching-Kang; Sin, Chor-Yiu. On prediction errors in regression models with nonstationary regressors. Time Series and Related Topics, 60--71, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000950.

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