Testing for Mean Reversion in Heteroskedastic Data II: Autoregression Tests Based on Gibbs-Sampling-Augmented Randomization

Abstract

A decade ago Fama and French (1988) estimated that 40% of variation in stock returns was predictable over horizons of 3-5 years, which they attributed to a mean reverting stationary component in prices. While it has been clear that the Depression and war years exert a strong influence on these estimates, it has not been clear whether the large returns of that period contribute to the information in the data or rather are a source of noise to be discounted in estimation. This paper uses the Gibbs-sampling-augmented randomization methodology to address the problem of heteroskedasticity in estimation of multi-period return autoregressions. Extending the sample period to 1995, we find little evidence of mean reversion. Examining subsamples, only 1926-46 provides any evidence of mean reversion, while the post war period is characterized by mean aversion. A test of structural change suggests that this difference between pre and post war periods is significant.