Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families

2026-06-01

AI Summary

This work addresses nonstationary time series characterized by instantaneous effects, nonlinear dynamics, and frequent regime switches by proposing the FlowMSM framework. Under exponential-family noise and a Markov switching mechanism, FlowMSM is the first to achieve simultaneous identifiability of latent regimes and their associated causal structures. The method establishes identifiability theory for a class of Markov-switching models incorporating time-dependent mechanisms, lagged dependencies, and instantaneous effects, and integrates any stationary causal discovery algorithm to recover regime-specific causal graphs. Experiments on both synthetic and real-world financial and economic data demonstrate its effectiveness in accurately identifying latent states and their corresponding causal structures. Notably, non-temporal causal mixture models are encompassed as a special case within this framework.

Abstract

Temporal systems often exhibit non-stationary behaviour, such as seasonal climate variation or glucose fluctuations in patients with type-1 diabetes. One way to model non-stationarity is through discrete latent regimes, i.e., stationary segments of time. Such systems induce a Markov Switching Model (MSM), a class of Hidden Markov Models with autoregressive dependencies among latent regimes and observed variables. Identifying latent regimes is challenging in the presence of frequent regime switches and nonlinear and non-Gaussian dynamics, particularly when there are instantaneous effects between the variables, e.g., due to slow rates of measurements. In this work, we establish the identifiability of both latent regimes and regime-dependent causal structures under temporal regime dependencies, nonlinear lagged and instantaneous effects, and independent noise from the exponential family. Our identifiability theory subsumes non-temporal mixtures of causal models. Furthermore, we introduce FlowMSM, a regime detection framework that can be paired with any stationary causal discovery method to recover regime-dependent causal structures. Experiments on synthetic benchmarks and a financial economics dataset demonstrate the effectiveness of our approach to detect latent regimes and discover causal structures from non-stationary time series.

Problem

• Markov Switching Models
• identifiability
• instantaneous effects
• non-stationary time series
• causal discovery

Innovation

• Markov Switching Models
• Identifiability
• Instantaneous Effects
• Causal Discovery
• Exponential Family