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Sequential Bayesian Inference for Vector Autoregressions with Stochastic Volatility

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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.

Suggested Citation

  • Mark Bognanni & John Zito, 2019. "Sequential Bayesian Inference for Vector Autoregressions with Stochastic Volatility," Working Papers 19-29, Federal Reserve Bank of Cleveland.
    • Handle: RePEc:fip:fedcwq:86647
    DOI: 10.26509/frbc-wp-201929
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    Cited by:

    1. Edward P. Herbst & Fabian Winkler, 2021. "The Factor Structure of Disagreement," Finance and Economics Discussion Series 2021-046, Board of Governors of the Federal Reserve System (U.S.).

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    More about this item

    Keywords

    Vector autoregressions; sequential Monte Carlo; Rao-Blackwellization; particle filter; stochastic volatility;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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