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Boosting High Dimensional Predictive Regressions with Time Varying Parameters

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  • Kashif Yousuf
  • Serena Ng

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.

Suggested Citation

  • Kashif Yousuf & Serena Ng, 2019. "Boosting High Dimensional Predictive Regressions with Time Varying Parameters," Papers 1910.03109, arXiv.org.
  • Handle: RePEc:arx:papers:1910.03109
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    Cited by:

    1. Dalibor Stevanovic & Stéphane Surprenant & Philippe Goulet Coulombe, 2019. "How is Machine Learning Useful for Macroeconomic Forecasting?," CIRANO Working Papers 2019s-22, CIRANO.
    2. Gary Koop & Dimitris Korobilis, 2020. "Bayesian dynamic variable selection in high dimensions," Working Papers 2020_11, Business School - Economics, University of Glasgow.

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