Estimation of prediction error variance

An Hong-Zhi

Stochastic Processes and their Applications, 1982, vol. 13, issue 1, 39-43

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.

Keywords: Stationary; time; series; spectral; density; prediction; error; variance (search for similar items in EconPapers)
Date: 1982
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