Researchers in finance very often rely on highly persistent – nearly integrated – explanatory variables to predict returns. However, statistical inference in predictive regressions depends critically upon the stochastic properties of the posited explanatory variable, and in particular, of...

We present a simple dynamical model of stock index returns which is grounded on the ability of the Cyclically Adjusted Price Earning (CAPE) valuation ratio devised by Robert Shiller to predict long-horizon performances of the market. More precisely, we discuss a discrete time dynamics in which...