A Note on Mean‐squared Prediction Errors of the Least Squares Predictors in Random Walk Models

C. K. Ing

Journal of Time Series Analysis, 2001, vol. 22, issue 6, 711-724

Abstract: An asymptotic expression for the mean‐squared prediction error (MSPE) of the least squares predictor is obtained in the random walk model. It is shown that the term of order 1/n in this error, where n is the sample size, is twice as large as the one obtained from the first‐order autoregressive (AR(1)) model satisfying the stationary assumption. Moreover, while the correlation between the squares of the (normalized) regressor variable and normalized least squares estimator is asymptotically negligible in the stationary AR(1) model, we have found that the correlation has significantly negative value in the random walk model. To obtain these results, a new methodology, which is found to be useful in dealing with the moment properties of a strongly dependent process, is introduced.

Date: 2001
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