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.

翻译：本文推导了用于拟合各类异方差时间序列模型的随机变分推理算法。我们考察了高斯响应、t分布响应以及偏t分布响应的GARCH模型，并采用高斯变分近似密度对其进行拟合。基于控制变量法或重参数化技巧，我们实现了高效的随机梯度上升流程，并证明所提方案可为马尔可夫链蒙特卡洛采样提供快速且精确的替代方案。此外，我们提出了适用于高效投资组合构建与动态资产配置的变分算法序贯更新版本。