A Bayes Inference Approach to Testing Mean Reversion in the Swedish Stock Market

Abstract

This paper makes use of the Bayesian approach to test for mean reversion in the Swedish stock market via Gibbs sampling. We use a sample of eighty years of monthly Swedish stock market returns including dividends from December 1918 to December 1998. We test for mean reversion in the short-run using two up to twelve months' horizons and in the long-run using yearly horizons up to ten years. Previous evidence of mean reversion via variance ratio is controversial because the test is only valid under the assumption of constant expected return. The return series from financial markets are well known to exhibit time varying volatility. Thus, the findings of mean reversion in the Swedish stock market might be explained by time-variation, or regime switches, in volatility. Hence we assume two regimes: low and high volatility and we let the volatility regimes be described by a two-state Hidden Markov Model, were the states are unobservable parameters. The Bayesian Gibbs sampling framework is advantageous as is allows us to make statistical inference of the parameters of interest without direct estimation of the likelihood function. This is pleasant property as we avoid the problem of estimating sometimes difficult likelihood functions. The result of our analysis offsets previous findings of mean reversion in the Swedish stock market. By simply account for the heteroscedasticty of the data and taking estimation bias into account we can not find any support of mean reversion. On the contrary the Swedish stock market can be characterized by two regimes, a tranquil and a volatile, and within the regimes the stock market is random. This finding is in line with what have been found on the U.S. stock market 1926-1986. Thus, accounting for time-variation in volatility and estimation bias improves the variance ratio test.