Sparse Bayesian vector autoregressions in huge dimensions

Abstract

We develop a Bayesian vector autoregressive (VAR) model with multivariate stochastic volatility that is capable of handling vast dimensional information sets. Three features are introduced to permit reliable estimation of the model. First, we assume that the reduced-form errors in the VAR feature a factor stochastic volatility structure, allowing for conditional equation-by-equation estimation. Second, we apply recently developed global-local shrinkage priors to the VAR coefficients to cure the curse of dimensionality. Third, we utilize recent innovations to efficiently sample from high-dimensional multivariate Gaussian distributions. This makes simulationbased fully Bayesian inference feasible when the dimensionality is large but the time series length is moderate. We demonstrate the merits of our approach in an extensive simulation study and apply the model to US macroeconomic data to evaluate its forecasting capabilities.

Regional output growth in the United Kingdom: More timely and higher frequency estimates from 1970

“…The blocks of the MCMC algorithm relating to the Dirichlet-Laplace prior are derived in Bhattacharya et al (2015). Kastner and Huber (2017) use this algorithm in a large VAR. Sections 4 and 6.4 of Kastner and Huber discuss its computational properties.…”

Inducing Sparsity and Shrinkage in Time-Varying Parameter Models

“…Then the TVP regression algorithm of the preceding sub-section can be applied one equation at a time. Equation-by-equation estimation of VARs is done in several recent papers using transformations similar to the one used here (see, e.g., Carriero et al, 2016;Kastner and Huber, 2017;Koop et al, 2019) and the reader is refered to these papers for further details about the computational advantages of this approach. With macroeconomic data it is often important to add stochastic volatility, which leads us to the TVP-VAR-SV specification described in this section.…”

“…As noted in Carriero et al (2016); Kastner and Huber (2017); Koop et al (2019), computation is greatly simplified if the model is transformed so that the errors in different equations are independent of one another. This can be achieved by augmenting the i th equation in the system with the contemporaneous values of the first i − 1 elements in y t .…”

Bayesian Vector Autoregressions

“…This is done by assuming that the reduced-form residuals have a factor stochastic volatility structure (which allows for conditional equationby-equation estimation) and by applying a Dirichlet-Laplace prior (Bhattacharya et al, 2015b) to the VAR coefficients that heavily shrinks the coefficients towards zero while still allowing for some non-zero parameters. Kastner and Huber (2017) Markov-switching or structural-break models.…”