Multi-regime Markov-switching models with time-varying transition probabilities: An application to U.S. Treasury yields

Paper: arXiv 2605.14976

Authors: Samuel Modée, Yushu Li, Sjur Westgaard, Stein Andreas Bethuelsen

Abstract

This paper studies Markov-switching (MS) models with time-varying transition probabilities (TVTP) under various specifications of the transition probability matrix. Especially, we extend the two-regime common-variance setting of the Generalized Autoregressive Score (GAS) model from (Bazzi et al., 2017) to the general $K$-regime case with regime-specific means and variances. Our study contains comprehensive Monte Carlo simulations and we developed an open-source R package, \texttt{multiregimeTVTP}, for data simulation and parameter estimation. We find that the regime means, variances, and transition probabilities are reliably recovered, whereas the TVTP driving coefficients are harder to identify. Another finding from our paper is that the GAS score coefficient appears to be statistically non-identifiable, due to a ridge in the joint likelihood surface $(σ^2,A)$. In addition, we find that one-step point forecasts are remarkably robust to TVTP misspecification, but filtered regime probabilities are not, so correct specification matters most for characterizing regime dynamics rather than short-horizon forecasting. An empirical application to U.S. Treasury zero-coupon yield changes at four maturities (1961-2024) shows that an exogenous specification driven by the lagged yield level dominates the constant and lagged-change models in fit, while the GAS specification fails to converge, with $\hat{A}$ collapsing to zero, reflecting the same identifiability issue observed in simulation.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10 (capped from 7.0: no out-of-sample test; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper combines intensive mathematical derivation of Generalized Autoregressive Score (GAS) models and Markov-switching frameworks with an open-source R package and comprehensive empirical application to U.S. Treasury yields. It successfully balances rigorous statistical theory with practical model validation through Monte Carlo simulations and real-world backtesting.

Research Flowchart

  flowchart TD
    A[<b>Goal:</b> Analyze MS models with<br/>Time-Varying Transition Probabilities] --> B[<b>Methodology:</b> Extend GAS model<br/>to K-regime with TVTP]
    C[<b>Inputs:</b> U.S. Treasury zero-coupon<br/>yields (1961-2024)] --> D[<b>Computation:</b> Monte Carlo Simulations &<br/>R package 'multiregimeTVTP']
    B & D --> E[<b>Findings:</b> Identification challenges of GAS,<br/>robustness of forecasts vs.<br/>sensitive regime filtering]
    E --> F[<b>Conclusion:</b> Exogenous yields dominate<br/>constant/GAS models in empirical fit]

Cited References (29)

1. State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications (1999)
2. Stylized facts and regime changes: Are prices procyclical? (1995) — link
3. A M arkov switching model of the conditional volatility of crude oil futures prices (2002) — link
4. Asymptotic properties of the maximum likelihood estimator in regime-switching models with time-varying transition probabilities (2023) — link
5. A new approach to model regime switching (2017) — link
6. Regime Switching Modeling of Substance Use: Time-Varying and Second-Order M arkov Models and Individual Probability Plots (2016) — link
7. Choosing information variables for transition probabilities in a time-varying transition probability M arkov switching model (1998) — link
8. A M arkov Model of Switching-Regime ARCH (1994) — link

0 of 29 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.