Adaptive time series forecasting with markovian variance switching
Baptiste Abélès Joseph de Vilmarest Olivier Wintemberger
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.