Nonparametric Estimations in Long-horizon regressions with nonstationary covariates

Nonparametric Estimations in Long-horizon regressions with nonstationary covariates

Abstract: We consider predictability in long-horizon regression models with nonstationary predictors. In the presence of integrated predictor, the predictability is represented as the limiting form of the sum of covariances between long-horizon regressand and …rst di¤erences of the covariate. Kernel-based nonparametric estimator for predictability is considered. Under the null of no long horizon predictability, asymptotic mean squared errors and normality of the estimator are presented. As the horizon grows to longer horizons, convergence rate of the estimators becomes slower than the case of short-horizon model. Our results provide extensions of short-horizon inferences in Maynard and Shimotsu (2008) to long-horizon regressions. Consistency under the local alternatives is also analyzed.