Bayesian Dynamic Variable Selection in High Dimensions

Abstract

This article addresses the issue of inference in time-varying parameter regression models in the presence of many predictors and develops a novel dynamic variable selection strategy. The proposed variational Bayes dynamic variable selection algorithm allows for assessing at each time period in the sample which predictors are relevant (or not) for forecasting the dependent variable. The algorithm is used to forecast inflation using over 400 macroeconomic, financial, and global predictors, many of which are potentially irrelevant or short-lived. The new methodology is able to ensure parsimonious solutions to this high-dimensional estimation problem, which translate into excellent forecast performance.

Forecasting realized volatility of crude oil futures prices based on machine learning

“…Second, many exogenous and powerful predictors, such as macroeconomic and financial market indicators, are highly correlated, which can lead to an over-fitting problem and overshadowing of significant parameters through present multicollinearity. With variable selection methods, only the most relevant variables are selected as predictors, thus reducing the risk of over-fitting issues and improving the forecast accuracy (Campbell & Slack, 2008;Korobilis, 2017;Korobilis & Koop, 2020). Analyzing the systematic selection of variables also allows us to identify breakpoints offering additional insight on the variability of the statistical and economical benefit of including exogenous predictors in HAR frameworks.…”

Discussion of “Multivariate dynamic modeling for Bayesian forecasting of business revenue”

“…Within the context of DLM that the authors present (see Yanchenko et al, 1 equation (1)) our suggestion implies that some of the coefficients $$$ {\boldsymbol{\theta}}_t $$$ may be zero in some time periods but not in others. This is the so‐called dynamic variable selection problem in statistics, and recently Koop and Korobilis 4 have developed a fast variational Bayes algorithm that allows to select among hundreds of predictors each time period.…”

Nonlinearities in macroeconomic tail risk through the lens of big data quantile regressions

“…Since $$$ K $$$ and $$$ T $$$ can be large, the dimension of the problem quickly becomes intractable. Again, our approach could handle such a situation well and several recent papers advocate using VB to carry out estimation and inference in TVP regression models (see Koop & Korobilis, 2023a). By contrast, MCMC estimation of such models is possible but requires sophisticated tricks or other approximations to speed up computation (for a recent contribution that uses singular value decompositions, see Hauzenberger et al, 2022).…”