Abstract
This chapter discusses the properties of estimates of the mean square error of prediction in autoregressive models. A selection criterion is used to choose a suitable finite order approximation to the infinite order autoregression. There are several criteria available: final prediction error method of Akaike; AIC, an information criterion; and the criterion autoregressive transfer function method of Parzen. All of these methods require an estimate of the mean error of one-step-ahead prediction when an optimal predictor of finite memory is used. The chapter also discusses the bias to terms of order n-1 of several estimates of the mean square error of one-step-ahead prediction for an optimal predictor of finite memory. In the estimates, the autoregressive coefficients, forming the optimal predictor of finite memory, are estimated by regression methods. The chapter describes estimates of the autoregressive coefficients, constructed from both biased and unbiased estimates of the population covariances.
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