The predictive power of the present value model of stock prices

Using monthly data from 1926:01 to 2003:12 for the United States, this paper examines the predictability of real stock prices based on the dividend-price ratio. In particular, we focus on estimating and forecasting a nonlinear exponential smooth autoregressive model (ESTAR). One motivation for nonlinearity in asset markets is the presence of transaction costs, which result in a nonlinear adjustment process towards equilibrium through arbitrage. Using a novel approach that allows for the joint testing of nonlinearity and nonstationarity, we are able to reject the null hypothesis of linearity and that of a nonlinear unit root. We also find evidence of a nonlinear cointegrating relationship between stock prices and dividends where the error correction term follows a globally stationary ESTAR process. This evidence together with nonlinear impulse response functions, which show that large deviations have faster speeds of mean reversion than small deviations indicates that while stock prices may reflect their fundamentals in the long run, they may deviate substantially from their fundamentals for periods of time. Using an ESTAR-EGARCH model of the dividend-price ratio we find empirical support for in-sample and out-of-sample long-horizon predictability, and we explain why it is often difficult to exploit this predictability using real-time forecasts.