# Modeling Regime Shifts in Multiple Time Series

arXiv: https://arxiv.org/abs/2109.09692 · HTML: https://mlsanity.com/paper/2109.09692/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 20 Sep 2021.

## Builds on (most cited first, 10 of 10)

- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Attributed Graph Clustering: A Deep Attentional Embedding Approach](https://mlsanity.com/paper/1906.06532/) (2019)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [Spatiotemporal Co-attention Recurrent Neural Networks for Human-Skeleton Motion Prediction](https://mlsanity.com/paper/1909.13245/) (2019)
- [Hierarchical Long Short-Term Concurrent Memory for Human Interaction Recognition](https://mlsanity.com/paper/1811.00270/) (2018)
- [A Comparative Analysis of Community Detection Algorithms on Artificial Networks](https://mlsanity.com/paper/1608.00763/) (2016)
- [Neural ODEs for Informative Missingness in Multivariate Time Series](https://mlsanity.com/paper/2005.10693/) (2020)
- [Time series cluster kernels to exploit informative missingness and incomplete label information](https://mlsanity.com/paper/1907.05251/) (2019)

## Built on by (most cited first, 2 of 2)

- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [Modeling Dynamic Mixtures of Time-Delay Systems from Streaming Time Series](https://mlsanity.com/paper/2605.26191/) (2026)

## Abstract (arXiv)

We investigate the problem of discovering and modeling regime shifts in an ecosystem comprising multiple time series known as co-evolving time series. Regime shifts refer to the changing behaviors exhibited by series at different time intervals. Learning these changing behaviors is a key step toward time series forecasting. While advances have been made, existing methods suffer from one or more of the following shortcomings: (1) failure to take relationships between time series into consideration for discovering regimes in multiple time series; (2) lack of an effective approach that models time-dependent behaviors exhibited by series; (3) difficulties in handling data discontinuities which may be informative. Most of the existing methods are unable to handle all of these three issues in a unified framework. This, therefore, motivates our effort to devise a principled approach for modeling interactions and time-dependency in co-evolving time series. Specifically, we model an ecosystem of multiple time series by summarizing the heavy ensemble of time series into a lighter and more meaningful structure called a textitmapping grid. By using the mapping grid, our model first learns time series behavioral dependencies through a dynamic network representation, then learns the regime transition mechanism via a full time-dependent Cox regression model. The originality of our approach lies in modeling interactions between time series in regime identification and in modeling time-dependent regime transition probabilities, usually assumed to be static in existing work.