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Journal Article

When are Variance Ratio Tests for Serial Dependence Optimal?

Jon Faust
Econometrica
Vol. 60, No. 5 (Sep., 1992), pp. 1215-1226
Published by: The Econometric Society
DOI: 10.2307/2951545
Stable URL: http://www.jstor.org/stable/2951545
Page Count: 12
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When are Variance Ratio Tests for Serial Dependence Optimal?
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Abstract

This paper considers a class of statistics that can be written as the ratio of the sample variance of a filtered time series to the sample variance of the original series. Any such statistic is shown to be optimal under normality for testing a null of white noise against some class of serially dependent alternatives. A simple characterization of the class of alternative models is provided in terms of the filter upon which the statistic is based. These results are applied to demonstrate that a variance ratio test for mean reversion is an optimal test for mean reversion and to illustrate the forms of mean reversion it is best at detecting.

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