Econometrica: Sep, 1992, Volume 60, Issue 5

When are Variance Ratio Tests for Serial Dependence Optimal?

https://doi.org/0012-9682(199209)60:5<1215:WAVRTF>2.0.CO;2-J
p. 1215-1226

Jon Faust

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.