Working Paper

Sequential Bayesian Inference for Vector Autoregressions with Stochastic Volatility

Abstract: We develop a sequential Monte Carlo (SMC) algorithm for Bayesian inference in vector autoregressions with stochastic volatility (VAR-SV). The algorithm builds particle approximations to the sequence of the model’s posteriors, adapting the particles from one approximation to the next as the window of available data expands. The parallelizability of the algorithm’s computations allows the adaptations to occur rapidly. Our particular algorithm exploits the ability to marginalize many parameters from the posterior analytically and embeds a known Markov chain Monte Carlo (MCMC) algorithm for the model as an effective mutation kernel for fighting particle degeneracy. We show that, relative to using MCMC alone, our algorithm increases the precision of inference while reducing computing time by an order of magnitude when estimating a medium-scale VAR-SV model.

Keywords: Vector autoregressions; sequential Monte Carlo; Rao-Blackwellization; particle filter; stochastic volatility;

JEL Classification: C11; C32; C51; E17;

https://doi.org/10.26509/frbc-wp-201929

Bibliographic Information

Provider: Federal Reserve Bank of Cleveland

Part of Series: Working Papers

Publication Date: 2019-12-16

Number: 19-29