On The Informational Content Of Asset Prices

What is the appropriate amount of past information to use in forecasting univariate linear processes? This paper proposes a non-parametric measure useful for sample size selection involving the data's asymptotic pre-dictability (AP). It is shown that the AP of a strictly stationary process is decreasing in its entropy rate. The finite-sample analog of the AP measure is the sample's entropy normalized by its alphabet size. First, Monte Carlo simulations of stationary pdf's indicate that AP increases with sample size, suggesting that "more is better". Second, computing the AP of long series of daily stock index, foreign exchange and interest rate returns suggests that AP varies non-monotonically with sample size. Moreover, the evolution of AP is characterized by strong breaks and øuctuations over time. The computa-tional framework allows a concrete comparison of the informational content of different datasets and their relative predictability.