Econometrica: Sep 1992, Volume 60, Issue 5

When are Variance Ratio Tests for Serial Dependence Optimal?<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.

Log In To View Full Content