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Estimation of prediction error variance

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  • Hong-Zhi, An

Abstract

This note considers an estimate of the variance of the prediction error for a normal stationary time series based on the periodogram. It is shown that as T --> [infinity], the estimate converges almost surely to [sigma]2, the variance of the prediction error for the best linear predictor. By applying a result of Hannan [2] it thus follows that if in fitting an autoregression to the data x(1),...,x(T) the order k is greatly overstated, then the resultant estimate [sigma]2k of [sigma]2 will be biased downward.

Suggested Citation

  • Hong-Zhi, An, 1982. "Estimation of prediction error variance," Stochastic Processes and their Applications, Elsevier, vol. 13(1), pages 39-43, July.
    • Handle: RePEc:eee:spapps:v:13:y:1982:i:1:p:39-43
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