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.

翻译：GARCH族模型的贝叶斯估计通常通过蒙特卡洛采样实现。变分推断作为复杂机器学习模型中贝叶斯推断的稳健方法正日益受到关注与重视，然而其在计量经济学与金融领域的应用仍然有限。本文探讨了变分推断在类GARCH模型中作为蒙特卡洛采样的可靠且可行替代方案的程度。通过一项涉及标普500指数成分股的大规模实验，结合多种变分推断优化器、各类波动率模型及案例研究，我们证明变分推断是一种具有吸引力、校准效果显著且具备竞争力的贝叶斯学习方法。