Real Stock Returns: Non-Normality, Seasonality, and Volatility Persistence, But No Predictability

We investigate persistence in CRSP monthly real stock returns, using a statespace model with symmetric stable disturbances. The non-Gaussian state-space model is estimated by maximum likelihood, using the optimal filtering algorithm given by Sorenson and Alspach (1971). Volatility seasonals and volatility persistence are quite strong. The conditional distribution has a stable a of 1.89, and normality is strongly rejected. However, stock returns do not contain a significant mean-reverting component. The optimal predictor is the unconditional expectation of the series, which we estimate to be 9.2 percent per annum.