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

2026-05-14

AI Summary

This study addresses the specification, identification, and estimation of time-varying transition probabilities (TVTP) in multi-state Markov-switching models, with particular emphasis on parameter identifiability under heteroskedastic regimes and the consequences of model misspecification. The work innovatively extends the generalized autoregressive score (GAS)-driven TVTP framework from the two-state homoskedastic case to a K-state heteroskedastic setting and introduces the open-source R package multiregimeTVTP to facilitate simulation and estimation. Theoretical analysis reveals that GAS score coefficients are unidentified due to ridge-like structures in the likelihood surface. Monte Carlo experiments demonstrate that regime-specific means, variances, and transition probabilities can be reliably recovered, though TVTP coefficients remain difficult to estimate. Empirically, a TVTP model driven by exogenous lagged interest rates significantly outperforms benchmark specifications in fitting U.S. Treasury yield data; while short-term forecasts prove robust to TVTP misspecification, filtered regime probabilities are highly sensitive to it.

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.

Problem

• Markov-switching models
• time-varying transition probabilities
• parameter identifiability
• regime dynamics
• GAS models

Innovation

• Markov-switching
• time-varying transition probabilities
• Generalized Autoregressive Score
• regime-specific variance
• parameter identifiability