Stochastic Variational Inference for GARCH Models

TL;DR

This paper develops stochastic variational inference algorithms for fitting heteroskedastic time series models like GARCH, offering a fast, accurate alternative to MCMC, with applications in portfolio management.

Contribution

It introduces efficient stochastic variational inference methods for GARCH models, including sequential updating algorithms for dynamic financial applications.

Findings

Fast and accurate inference compared to MCMC

Effective sequential updating for portfolio management

Applicability to Gaussian, t, and skew-t GARCH models

Abstract

Stochastic variational inference algorithms are derived for fitting various heteroskedastic time series models. We examine Gaussian, t, and skew-t response GARCH models and fit these using Gaussian variational approximating densities. We implement efficient stochastic gradient ascent procedures based on the use of control variates or the reparameterization trick and demonstrate that the proposed implementations provide a fast and accurate alternative to Markov chain Monte Carlo sampling. Additionally, we present sequential updating versions of our variational algorithms, which are suitable for efficient portfolio construction and dynamic asset allocation.