Title: Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families

Abstract:

Non-stationary behavior is a common characteristic of temporal systems, manifesting in phenomena such as seasonal climate shifts or blood glucose variations in individuals with type-1 diabetes. A viable approach to capturing this non-stationarity involves modeling the system through discrete latent regimes, which represent stationary intervals within the timeline. These systems are formalized as Markov Switching Models (MSMs), a specific category of Hidden Markov Models that incorporate autoregressive dependencies linking latent regimes to observed variables.

Accurately identifying these latent regimes presents significant challenges, particularly when the system experiences frequent regime transitions, exhibits nonlinear and non-Gaussian dynamics, or features instantaneous effects between variables—often resulting from slow measurement rates. In this study, we prove the identifiability of both the latent regimes and their associated causal structures. This proof holds under conditions of temporal regime dependencies, nonlinear lagged and instantaneous effects, and independent noise drawn from the exponential family. Our theoretical framework for identifiability extends to include non-temporal mixtures of causal models.

Additionally, we present FlowMSM, a regime detection framework designed to integrate with any stationary causal discovery method to uncover regime-specific causal structures. The efficacy of our proposed approach is validated through experiments on synthetic benchmarks as well as a dataset from financial economics, demonstrating its capability to effectively detect latent regimes and extract causal structures from non-stationary time series.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC