Regime-Switching Stock Returns and Mean Reversion

We estimate a well-specified two-state regime-switching model for Danish stock returns. The model identifies two regimes which have low return-low volatility and high return-high volatility, respectively. The low return-low volatility regime dominated, except in a few, short episodes, until the beginning of the 70s whereas the 80s and 90s have been characterized by high return and high volatility. We propose an alternative test of mean reversion which allows for multiple regimes with potentially different constant and autoregressive terms and different volatility. Using this test procedure we find mean reversion at 10% but not at 5% significance level which is weaker evidence than produced by estimating a standard autoregressive model for returns. Furthermore, when analyzing contributions of the two regimes we find that the indication of mean reversion is due to the recent high return-high volatility regime only.