Modeling Regime Shifts in Multiple Time Series

TL;DR

This paper introduces a unified framework for modeling regime shifts in multiple co-evolving time series by capturing interactions and time-dependent behaviors, improving regime detection and transition modeling.

Contribution

It proposes a novel approach using a mapping grid, dynamic networks, and Cox regression to model interactions and time-dependent regime transitions in multivariate time series.

Findings

Effective modeling of regime shifts in multiple time series.

Improved detection of regime transitions with time-dependent probabilities.

Unified framework handling data discontinuities and inter-series relationships.

Abstract

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 \textit{mapping 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.