# Adaptive time series forecasting with markovian variance switching

arXiv: https://arxiv.org/abs/2402.14684 · HTML: https://mlsanity.com/paper/2402.14684/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 22 Feb 2024.

## Builds on (most cited first, 9 of 9)

- [Online Natural Gradient as a Kalman Filter](https://mlsanity.com/paper/1703.00209/) (2017)
- [Adaptive Methods for Short-Term Electricity Load Forecasting During COVID-19 Lockdown in France](https://mlsanity.com/paper/2009.06527/) (2020)
- [Variational Bayes under Model Misspecification](https://mlsanity.com/paper/1905.10859/) (2019)
- [Efficient tracking of a growing number of experts](https://mlsanity.com/paper/1708.09811/) (2017)
- [Variational Inference and Learning of Piecewise-linear Dynamical Systems](https://mlsanity.com/paper/2006.01668/) (2020)
- [Stochastic Online Optimization using Kalman Recursion](https://mlsanity.com/paper/2002.03636/) (2020)
- [Viking: Variational Bayesian Variance Tracking](https://mlsanity.com/paper/2104.10777/) (2021)
- [Kalman Recursions Aggregated Online](https://mlsanity.com/paper/2002.12173/) (2020)
- [An On-line Variational Bayesian Model for Multi-Person Tracking from Cluttered Scenes](https://mlsanity.com/paper/1509.01520/) (2015)

## Built on by (most cited first, 1 of 1)

- [A unifying framework for generalised Bayesian online learning in non-stationary environments](https://mlsanity.com/paper/2411.10153/) (2024)

## Abstract (arXiv)

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.