Asymptotic Properties of an Estimate of the Prediction Error Variance

An estimate of the variance of the prediction error for a linear stationary time series is constructed by using only a part, ?₀, ?₁,…, ?_M, of the sample autocovariance sequence, where M increases with T, the length of the time series observed. M increases as T^α (α < ¹₄). Under a higher moment condition, but not assuming Gaussianity, the estimate obtained is shown to be strongly consistent and asymptotically normal. The asymptotic variance of the estimation error is also obtained.