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, 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 fast and accurate variational Bayes methods to approximate the posterior distribution of the states and parameters in factor stochastic volatility models. The second contribution 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.
翻译:高维多变量系数多变性模型的估测和预测是一个重要和活跃的研究领域,因为这种模型可以代表多变量多变性波动。Bayesian对因素随机波动模型的推论通常由Markov链 Monte Carlo 方法进行,通常由粒子Markov链 Monte Carlo 方法进行,由于涉及大量参数和潜伏状态,高维或长时间序列的粒子Markov链 Monte Carlo通常缓慢。我们的文章做出了两项贡献。第一是提出快速和准确的变异贝斯方法,以近似因素随机变化波动模型中状态和参数的后方分布。第二是推广这一批方法,以便在新的观测到达时为预测制定快速连续变化更新。这些方法用于模拟和真实的数据集,并显示与最新的粒子Markov链 Monte Carlo方法相比,产生非常近似的误判和预测,但速度要快得多。