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Bayesian Rank Selection in Multivariate Regression

Author

Listed:
  • Bin Jiang
  • Anastasios Panagiotelis
  • George Athanasopoulos
  • Rob Hyndman
  • Farshid Vahid
Abstract
Estimating the rank of the coefficient matrix is a major challenge in multivariate regression, including vector autoregression (VAR). In this paper, we develop a novel fully Bayesian approach that allows for rank estimation. The key to our approach is reparameterizing the coefficient matrix using its singular value decomposition and conducting Bayesian inference on the decomposed parameters. By implementing a stochastic search variable selection on the singular values of the coefficient matrix, the ultimate selected rank can be identified as the number of nonzero singular values. Our approach is appropriate for small multivariate regressions as well as for higher dimensional models with up to about 40 predictors. In macroeconomic forecasting using VARs, the advantages of shrinkage through proper Bayesian priors are well documented. Consequently, the shrinkage approach proposed here that selects or averages over low rank coefficient matrices is evaluated in a forecasting environment. We show in both simulations and empirical studies that our Bayesian approach provides forecasts that are better than those of the most promising benchmark methods, dynamic factor models and factor augmented VARs.

Suggested Citation

  • Bin Jiang & Anastasios Panagiotelis & George Athanasopoulos & Rob Hyndman & Farshid Vahid, 2016. "Bayesian Rank Selection in Multivariate Regression," Monash Econometrics and Business Statistics Working Papers 6/16, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2016-6
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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp06-16.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    singular value decomposition; model selection; vector autoregression; macroeconomic forecasting; dynamic factor models;
    All these keywords.

    JEL classification:

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

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