A simple approach for diagnosing instabilities in predictive regressions

We introduce a method for detecting the presence of structural breaks in the parameters of predictive regressions linking noisy variables such as stock returns to persistent predictors such as valuation ratios. Our approach relies on the least squares based squared residuals of the predictive regression and is straightforward to implement. The distributions of the two test statistics we introduce are shown to be free of nuisance parameters, valid under dependent errors, already tabulated in the literature and robust to the degree of persistence of the chosen predictor. Our proposed method is subsequently applied to the predictability of US stock returns.