Adaptive time series forecasting is essential for prediction under regime changes. Several classical methods assume linear Gaussian state space model (LGSSM) with variances constant in time. However, there are many real-world processes that cannot be captured by such models. We consider a state-space model with Markov switching variances. Such dynamical systems are usually intractable because of their computational complexity increasing exponentially with time; Variational Bayes (VB) techniques have been applied to this problem. In this paper, we propose a new way of estimating variances based on online learning theory; we adapt expert aggregation methods to learn the variances over time. We apply the proposed method to synthetic data and to the problem of electricity load forecasting. We show that this method is robust to misspecification and outperforms traditional expert aggregation.

翻译：自适应时间序列预测对于在机制变化下进行预测至关重要。几种经典方法假设线性高斯状态空间模型（LGSSM）的方差随时间恒定。然而，许多现实世界的过程无法用此类模型捕捉。我们考虑一个具有马尔可夫切换方差的状态空间模型。这类动态系统通常因其计算复杂度随时间呈指数增长而难以处理；变分贝叶斯（VB）技术已被应用于该问题。本文提出了一种基于在线学习理论的新方差估计方法；我们采用专家聚合方法来随时间学习方差。我们将所提方法应用于合成数据以及电力负荷预测问题。结果表明，该方法对模型误设具有鲁棒性，并且优于传统专家聚合方法。