Using annual data for 1872-1997, this paper re-examines the predictability of real stock prices based on price-dividend and price-earnings ratios. In line with the extant literature, we find significant evidence of increased long-horizon predictability; that is, the hypothesis that the current value of a valuation ratio is uncorrelated with future stock price changes cannot be rejected at short horizons but can be rejected at longer horizons based on bootstrapped critical values constructed from linear representations of the data. While increased statistical power at long horizons in finite samples provides a possible explanation for the pattern of predictability in the data, we find via Monte Carlo simulations that the power to detect predictability in finite samples does not increase at long horizons in a linear framework. An alternative explanation for the pattern of predictability in the data is nonlinearities in the underlying data-generating process. We consider exponential smooth-transition autoregressive models of the price-dividend and price-earnings ratios and their ability to explain the pattern of stock price predictability in the data.