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Predictive Quantile Regression with High-Dimensional Predictors: The Variable Screening Approach

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  • Hongqi Chen
  • Ji Hyung Lee

Abstract

This paper advances a variable screening approach to enhance conditional quantile forecasts using high-dimensional predictors. We have refined and augmented the quantile partial correlation (QPC)-based variable screening proposed by Ma et al. (2017) to accommodate $\beta$-mixing time-series data. Our approach is inclusive of i.i.d scenarios but introduces new convergence bounds for time-series contexts, suggesting the performance of QPC-based screening is influenced by the degree of time-series dependence. Through Monte Carlo simulations, we validate the effectiveness of QPC under weak dependence. Our empirical assessment of variable selection for growth-at-risk (GaR) forecasting underscores the method's advantages, revealing that specific labor market determinants play a pivotal role in forecasting GaR. While prior empirical research has predominantly considered a limited set of predictors, we employ the comprehensive Fred-QD dataset, retaining a richer breadth of information for GaR forecasts.

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  • Hongqi Chen & Ji Hyung Lee, 2024. "Predictive Quantile Regression with High-Dimensional Predictors: The Variable Screening Approach," Papers 2410.15097, arXiv.org.
  • Handle: RePEc:arx:papers:2410.15097
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    References listed on IDEAS

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    1. Kong, Yinfei & Li, Yujie & Zerom, Dawit, 2019. "Screening and selection for quantile regression using an alternative measure of variable importance," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 435-455.
    2. Galvao, Antonio F. & Kato, Kengo, 2016. "Smoothed quantile regression for panel data," Journal of Econometrics, Elsevier, vol. 193(1), pages 92-112.
    3. Zhang, Shucong & Zhou, Yong, 2018. "Variable screening for ultrahigh dimensional heterogeneous data via conditional quantile correlations," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 1-13.
    4. Michael W. McCracken & Serena Ng, 2016. "FRED-MD: A Monthly Database for Macroeconomic Research," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 574-589, October.
    5. Chiou, Hai-Tang & Guo, Meihui & Ing, Ching-Kang, 2020. "Variable selection for high-dimensional regression models with time series and heteroscedastic errors," Journal of Econometrics, Elsevier, vol. 216(1), pages 118-136.
    6. Eun Ryung Lee & Hohsuk Noh & Byeong U. Park, 2014. "Model Selection via Bayesian Information Criterion for Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 216-229, March.
    7. Guodong Li & Yang Li & Chih-Ling Tsai, 2015. "Quantile Correlations and Quantile Autoregressive Modeling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 246-261, March.
    8. Brownlees, Christian & Souza, André B.M., 2021. "Backtesting global Growth-at-Risk," Journal of Monetary Economics, Elsevier, vol. 118(C), pages 312-330.
    9. Mikkel Plagborg-Moller & Lucrezia Reichlin & Giovanni Ricco & Thomas Hasenzagl, 2020. "When Is Growth at Risk?," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 51(1 (Spring), pages 167-229.
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    11. Wang, Hansheng, 2009. "Forward Regression for Ultra-High Dimensional Variable Screening," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1512-1524.
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