Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area, because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian inference for factor stochastic volatility models is usually done by Markov chain Monte Carlo methods (often by particle Markov chain Monte Carlo methods), which are usually slow for high dimensional or long time series because of the large number of parameters and latent states involved. Our article makes two contributions. The first is to propose a fast and accurate variational Bayes methods to approximate the posterior distribution of the states and parameters in factor stochastic volatility models. The second is to extend this batch methodology to develop fast sequential variational updates for prediction as new observations arrive. The methods are applied to simulated and real datasets, and shown to produce good approximate inference and prediction compared to the latest particle Markov chain Monte Carlo approaches, but are much faster.

高维多元因子随机波动率模型中的估计和预测是一个重要且活跃的研究领域，因为此类模型允许对多元随机波动率进行简约表示。因子随机波动率模型的贝叶斯推断通常通过马尔可夫链蒙特卡罗方法（通常通过粒子马尔可夫链蒙特卡罗方法）完成，由于涉及大量参数和潜在状态，对于高维或长时间序列通常很慢。我们的文章有两个贡献。首先是提出一种快速准确的变分贝叶斯方法来近似因子随机波动率模型中状态和参数的后验分布。第二个是扩展此批处理方法，以开发快速连续变分更新，以便在新观测值到达时进行预测。这些方法应用于模拟和真实数据集，与最新的粒子马尔可夫链蒙特卡罗方法相比，可以产生良好的近似推理和预测，但速度要快得多。