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High dimensional predictive regressions are useful in wide range ofapplications. However, the theory is mainly developed assuming that the modelis stationary with time invariant parameters. This is at odds with theprevalent evidence for parameter instability in economic time series, buttheories for parameter instability are mainly developed for models with a smallnumber of covariates. In this paper, we present two $L_2$ boosting algorithmsfor estimating high dimensional models in which the coefficients are modeled asfunctions evolving smoothly over time and the predictors are locallystationary. The first method uses componentwise local constant estimators asbase learner, while the second relies on componentwise local linear estimators.We establish consistency of both methods, and address the practical issues ofchoosing the bandwidth for the base learners and the number of boostingiterations. In an extensive application to macroeconomic forecasting with manypotential predictors, we find that the benefits to modeling time variation aresubstantial and they increase with the forecast horizon. Furthermore, thetiming of the benefits suggests that the Great Moderation is associated withsubstantial instability in the conditional mean of various economic series.

Boosting High Dimensional Predictive Regressions with Time Varying Parameters