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

DOI:
https://doi.org/10.1090/S0002-9947-1995-1277143-9

MathSciNet review:
1277143

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Abstract | References | Similar Articles | Additional Information

Abstract: Assessing prediction error is a problem which arises in time series analysis. The distinction between the conditional prediction error and the unconditional prediction error 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 is nearly impossible. In particular, we use the correlation coefficient , where is an estimate of , as a measure of performance and show that where is the sample size and is some constant. Furthermore, the value of is large only when the process is extremely non-Gaussian or nearly nonstationary.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1277143-9

Keywords:
Conditional prediction error,
correlation,
cumulant,
higher-order spectrum,
non-Gaussian model

Article copyright:
© Copyright 1995
American Mathematical Society