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Bayesian factor-adjusted sparse regression

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  • Fan, Jianqing
  • Jiang, Bai
  • Sun, Qiang

Abstract

Many sparse regression methods rely on an assumption that the covariates are weakly correlated, which hardly holds in many economic and financial datasets. To relax this assumption, we model the strongly correlated covariates by a factor structure: strong correlations among covariates are modeled by common factors, while the remaining variations of covariates are modeled as idiosyncratic components. We then propose a factor-adjusted sparse regression model and develop a semi-Bayesian estimation method for it. Posterior contraction rate and model selection consistency are established by a non-asymptotic analysis. Experimental studies show that the proposed method outperforms its Lasso analogue, manifests insensitivity to overestimates of the number of common factors, pays a negligible price when covariates are uncorrelated, scales up well with increasing sample size, dimensionality and sparsity, and converges fast to the posterior distribution. An application to the U.S. bond risk premia lends further support to the proposed model and method.

Suggested Citation

  • Fan, Jianqing & Jiang, Bai & Sun, Qiang, 2022. "Bayesian factor-adjusted sparse regression," Journal of Econometrics, Elsevier, vol. 230(1), pages 3-19.
  • Handle: RePEc:eee:econom:v:230:y:2022:i:1:p:3-19
    DOI: 10.1016/j.jeconom.2020.06.012
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    1. Helena Chuliá & Sabuhi Khalili & Jorge M. Uribe, 2024. "Monitoring time-varying systemic risk in sovereign debt and currency markets with generative AI," IREA Working Papers 202402, University of Barcelona, Research Institute of Applied Economics, revised Feb 2024.

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    More about this item

    Keywords

    Factor model; Bayesian sparse regression; Posterior contraction; Model selection;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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