Variational Bayesian Inference in Large Vector Autoregressions with Hierarchical Shrinkage

29 Pages Posted: 24 Jan 2019

See all articles by Deborah Gefang

Deborah Gefang

University of Leicester - Department of Economics; University of Leicester

Gary Koop

University of Strathclyde, Glasgow - Strathclyde Business School - Department of Economics

Aubrey Poon

University of Strathclyde - Centre for Applied Macroeconomic Analysis

Date Written: January 24, 2019

Abstract

Many recent papers in macroeconomics have used large Vector Autoregressions (VARs) involving a hundred or more dependent variables. With so many parameters to estimate, Bayesian prior shrinkage is vital in achieving reasonable results. Computational concerns currently limit the range of priors used and render difficult the addition of empirically important features such as stochastic volatility to the large VAR. In this paper, we develop variational Bayes methods for large VARs which overcome the computational hurdle and allow for Bayesian inference in large VARs with a range of hierarchical shrinkage priors and with time-varying volatilities. We demonstrate the computational feasibility and good forecast performance of our methods in an empirical application involving a large quarterly US macroeconomic data set.

Keywords: Variational inference, Vector Autoregression, Stochastic Volatility, Hierarchical Prior, Forecasting

JEL Classification: C11, C32, C53

Suggested Citation

Gefang, Deborah and Koop, Gary and Poon, Aubrey, Variational Bayesian Inference in Large Vector Autoregressions with Hierarchical Shrinkage (January 24, 2019). CAMA Working Paper No. 08/2019. Available at SSRN: https://ssrn.com/abstract=3321510 or http://dx.doi.org/10.2139/ssrn.3321510

Deborah Gefang

University of Leicester - Department of Economics ( email )

Department of Economics
Leicester LE1 7RH, Leicestershire LE1 7RH
United Kingdom

University of Leicester ( email )

University Road
Leicester, LE1 7RH
United Kingdom

Gary Koop

University of Strathclyde, Glasgow - Strathclyde Business School - Department of Economics ( email )

100 Cathedral Street
Glasgow G4 0LN
United Kingdom

Aubrey Poon (Contact Author)

University of Strathclyde - Centre for Applied Macroeconomic Analysis ( email )

16 Richmond Street
Glasgow 1XQ, Scotland
United Kingdom

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