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Variable Selection in High Dimensional Linear Regressions with Parameter Instability

Author

Listed:
  • Alexander Chudik
  • M. Hashem Pesaran
  • Mahrad Sharifvaghefi

Abstract

This paper considers the problem of variable selection allowing for parameter instability. It distinguishes between signal and pseudo-signal variables that are correlated with the target variable, and noise variables that are not, and investigates the asymptotic properties of the One Covariate at a Time Multiple Testing (OCMT) method proposed by Chudik et al. (2018) under parameter insatiability. It is established that OCMT continues to asymptotically select an approximating model that includes all the signals and none of the noise variables. Properties of post selection regressions are also investigated, and in-sample fit of the selected regression is shown to have the oracle property. The theoretical results support the use of unweighted observations at the selection stage of OCMT, whilst applying down-weighting of observations only at the forecasting stage. Monte Carlo and empirical applications show that OCMT without down-weighting at the selection stage yields smaller mean squared forecast errors compared to Lasso, Adaptive Lasso and boosting.

Suggested Citation

  • Alexander Chudik & M. Hashem Pesaran & Mahrad Sharifvaghefi, 2020. "Variable Selection in High Dimensional Linear Regressions with Parameter Instability," Globalization Institute Working Papers 394, Federal Reserve Bank of Dallas, revised 05 Aug 2024.
    • Handle: RePEc:fip:feddgw:88638
    DOI: 10.24149/gwp394r3
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    References listed on IDEAS

    as
    1. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    2. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
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    Cited by:

    1. Christopher F Baum & Andrés Garcia-Suaza & Miguel Henry & Jesús Otero, 2024. "Drivers of COVID-19 in U.S. counties: A wave-level analysis," Boston College Working Papers in Economics 1067, Boston College Department of Economics.
    2. Skrobotov, Anton, 2024. "Time series forecasting under structural breaks," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 76, pages 120-139.

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    More about this item

    Keywords

    Lasso; one covariate at a time multiple testing (OCMT); parameter instability; variable selection; forecasting;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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