Abstract: If stock prices do not follow random walks, what processes do they follow? This question is important not only for forecasting purpose, but also for theoretical analyses and derivative pricing where a tractable model of the movement of underlying stock prices is needed. Although several models have been proposed to capture the predictability of stock returns, their empirical performances have not been evaluated. This paper evaluates some popular models using a Kalman Filter technique and finds that they have serious flaws. The paper then proposes an alternative parsimonious state-space model in which state variables characterize the stochastic movements of stock returns. Using equal-weighted CRSP monthly index, the paper shows that (1) this model fits the autocorrelations of returns well over both short and longer horizons and (2) although the forecasts obtained with the state-space model are based solely on past returns, they subsume the information in other potential predictor variables such as dividend yields.

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