Adaptive time series forecasting with markovian variance switching
This work addresses adaptive forecasting for real-world processes with changing variances, such as electricity load, but is incremental as it builds on existing expert aggregation methods.
The paper tackles the problem of time series forecasting under regime changes by proposing a new method for estimating variances using online learning theory and expert aggregation, applied to synthetic data and electricity load forecasting, showing robustness to misspecification and outperforming traditional expert aggregation.
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.