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Boosting high dimensional predictive regressions with time varying parameters

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  • Yousuf, Kashif
  • Ng, Serena
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 L2 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.

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  • Yousuf, Kashif & Ng, Serena, 2021. "Boosting high dimensional predictive regressions with time varying parameters," Journal of Econometrics, Elsevier, vol. 224(1), pages 60-87.
    • Handle: RePEc:eee:econom:v:224:y:2021:i:1:p:60-87
    DOI: 10.1016/j.jeconom.2020.08.003
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    Cited by:

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    3. Sun, Yuying & Hong, Yongmiao & Wang, Shouyang & Zhang, Xinyu, 2023. "Penalized time-varying model averaging," Journal of Econometrics, Elsevier, vol. 235(2), pages 1355-1377.
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    7. Ziwei Mei & Zhentao Shi, 2022. "On LASSO for High Dimensional Predictive Regression," Papers 2212.07052, arXiv.org, revised Jan 2024.
    8. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    9. Deshui Yu & Yayi Yan, 2023. "Joint dynamics of stock returns and cash flows: A time‐varying present‐value framework," Financial Management, Financial Management Association International, vol. 52(3), pages 513-541, September.
    10. Friedrich, Marina & Lin, Yicong, 2024. "Sieve bootstrap inference for linear time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 239(1).
    11. Yu, Deshui & Chen, Li & Li, Luyang, 2023. "Time-varying predictability of the long horizon equity premium based on semiparametric regressions," Economics Letters, Elsevier, vol. 224(C).

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    More about this item

    Keywords

    L2 boosting; Forecasting; Locally stationary; Parameter instability; Sparsity;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

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