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Transactions of the American Mathematical Society

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Assessing prediction error in autoregressive models

Authors: Ping Zhang and Paul Shaman
Journal: Trans. Amer. Math. Soc. 347 (1995), 627-637
MSC: Primary 62M10; Secondary 62M20
MathSciNet review: 1277143
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Abstract: Assessing prediction error is a problem which arises in time series analysis. The distinction between the conditional prediction error $ e$ and the unconditional prediction error $ E(e)$ has not received much attention in the literature. Although one can argue that the conditional version is more practical, we show in this article that assessing $ e$ is nearly impossible. In particular, we use the correlation coefficient $ \operatorname{corr} (\hat e,e)$, where $ \hat e$ is an estimate of $ e$, as a measure of performance and show that $ {\lim _{T \to \infty }}\sqrt T \operatorname{corr} (\hat e,e) = C$ where $ T$ is the sample size and $ C > 0$ is some constant. Furthermore, the value of $ C$ is large only when the process is extremely non-Gaussian or nearly nonstationary.

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Keywords: Conditional prediction error, correlation, cumulant, higher-order spectrum, non-Gaussian model
Article copyright: © Copyright 1995 American Mathematical Society