A simple approach for diagnosing instabilities in predictive regressions

We introduce a method for detecting the presence of time variation and instabilities in the parameters of predictive regressions linking noisy variables such as stock returns to highly persistent predictors such as stock market valuation ratios. Our proposed approach relies on the least squares based squared residuals of the predictive regression and is trivial to implement. More importantly the distribution of our test statistic is shown to be free of nuisance parameters, is already tabulated in the literature and is robust to the degree of persistence of the chosen predictor. Our proposed method is subsequently applied to the predictability of monthly US stock returns with the dividend yield, dividend payout, earnings-price, dividend-price and book-to-market value ratios. Our results strongly support the presence of instabilities over the 1927-2013 period but also clearly point to the disappearance of these after the mid 50s. <br><br> Keywords; predictability of stock returns, structural breaks, CUSUMSQ, predictive regressions