Boosting high dimensional predictive regressions with time varying parameters

High dimensional predictive regressions are useful in wide range of applications. However, the theory is mainly developed assuming that model stationary with time invariant parameters. This at odds prevalent evidence for parameter instability economic series, but theories models a small number covariates. In this paper, we present two L2 boosting algorithms estimating high which coefficients modeled as functions evolving smoothly over and predictors locally stationary. The first method uses componentwise local constant estimators base learner, while second relies on linear estimators. We establish consistency both methods, address practical issues choosing bandwidth learners iterations. an extensive application to macroeconomic forecasting many potential predictors, find benefits modeling variation substantial they increase forecast horizon. Furthermore, timing suggests Great Moderation associated conditional mean various series.