On Assessing Prediction Error in Autoregressive Models

Abstract

Zhang and Shaman (Assessing prediction error in autoregressive models. Trans. Am. Math. Soc. 347, (1995), 627–37) pose the problem of estimating the conditional mean square one‐step‐ahead prediction error (CMOPE) for a Gaussian first‐order autoregressive process. They put forward a certain estimator (with small asymptotic bias) of CMOPE and propose that its effectiveness be judged by its asymptotic correlation with CMOPE. Unfortunately, the derivation of this correlation by Zhang and Shaman (1995) is incomplete. It is very difficult to complete this derivation. For this reason we use Monte Carlo simulation to gain some insight into the correlation of the estimator with CMOPE. The results of this simulation show that the estimator is extremely poor. We then propose an alternative estimator (with small asymptotic bias) of CMOPE which is shown from Monte Carlo simulation results to have higher large‐sample correlation with CMOPE than the estimator of CMOPE put forward by Zhang and Shaman (1995).