**Author: **Faust, Jon

**Source:** Econometrica, September 1992, v. 60, iss. 5, pp. 1215-26

**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 alternative class is provided. The results are used to show that a variance ratio test for mean reversion is an optimal test and to illustrate the forms of mean reversion it is best at detecting.

**Descriptors:** Time Series and Spectral Analysis (2116) Econometric and Statistical Methods and Models: Multivariate Analysis, Statistical Information Theory, and Other Special Inferential Problems; Queuing Theory; Markov Chains (2114) Distributed Correlated Disturbance Terms; Inferential Problems in Single Equation Models (2113) Econometric Methods: Single Equation Models: Time-Series Models (C220)

**paper:**

**program:**
[zip 20k]
DOS executable for calculating p-values for variance ratio test