Spurious Mean-Reversion of Stock Prices in the State-Space Model

In order to explain the U-shaped pattern of autocorrelations of stock returns i.e., autocorrelations starting around 0 for short-term horizons and becoming negative and then moving toward 0 for long-term horizons, researchers suggested the use of a state-space model consisting of an I(1) permanent component and an AR(1) stationary component, where the two components are assumed to be independent. They concluded that auto-regression coefficients derived from the state-space model follow a U-shape pattern and thus there is mean-reversion in stock prices. In this paper, we show that only negative autocorrelations are feasible under the assumption that the permanent component and the stationary component are independent in the state-space model. When the two components are allowed to be correlated in the state-space model, we show that the sign of the auto-regression coefficients is not restricted as negative. Monthly return data for all NYSE stocks for the period from 1926 to 2007 support the state-space model with correlated noise processes. However, the auto-regression coefficients of the ARIMA process, equivalent to the state-space model with correlated noise processes, do not follow a U-shaped pattern, but are always positive