Variational Inference for GARCH-family Models

TL;DR

This paper evaluates the effectiveness of Variational Inference as a practical and reliable alternative to Monte Carlo sampling for Bayesian estimation in GARCH-family models, especially in financial applications.

Contribution

It demonstrates that Variational Inference is a competitive, well-calibrated method for Bayesian inference in GARCH models through extensive experiments and case studies.

Findings

Variational Inference is well-calibrated and competitive.

It offers a feasible alternative to Monte Carlo sampling.

The method performs well across different models and optimizers.

Abstract

The Bayesian estimation of GARCH-family models has been typically addressed through Monte Carlo sampling. Variational Inference is gaining popularity and attention as a robust approach for Bayesian inference in complex machine learning models; however, its adoption in econometrics and finance is limited. This paper discusses the extent to which Variational Inference constitutes a reliable and feasible alternative to Monte Carlo sampling for Bayesian inference in GARCH-like models. Through a large-scale experiment involving the constituents of the S&P 500 index, several Variational Inference optimizers, a variety of volatility models, and a case study, we show that Variational Inference is an attractive, remarkably well-calibrated, and competitive method for Bayesian learning.