Boosting High Dimensional Predictive Regressions with Time Varying Parameters

TL;DR

This paper introduces two boosting algorithms for high-dimensional predictive regressions with time-varying parameters, addressing the challenge of non-stationarity in economic data and demonstrating their effectiveness in macroeconomic forecasting.

Contribution

The paper develops two novel $L_2$ boosting methods for high-dimensional models with smoothly evolving coefficients, extending existing theories to handle parameter instability.

Findings

Modeling time variation improves forecast accuracy.

Benefits increase with forecast horizon.

Economic instability correlates with the Great Moderation.

Abstract

High dimensional predictive regressions are useful in wide range of applications. However, the theory is mainly developed assuming that the model is stationary with time invariant parameters. This is at odds with the prevalent evidence for parameter instability in economic time series, but theories for parameter instability are mainly developed for models with a small number of covariates. In this paper, we present two $L_2$ boosting algorithms for estimating high dimensional models in which the coefficients are modeled as functions evolving smoothly over time and the predictors are locally stationary. The first method uses componentwise local constant estimators as base learner, while the second relies on componentwise local linear estimators. We establish consistency of both methods, and address the practical issues of choosing the bandwidth for the base learners and the number of boosting iterations. In an extensive application to macroeconomic forecasting with many potential predictors, we find that the benefits to modeling time variation are substantial and they increase with the forecast horizon. Furthermore, the timing of the benefits suggests that the Great Moderation is associated with substantial instability in the conditional mean of various economic series.