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.

翻译：本文研究在转移概率矩阵不同设定下具有时变转移概率(TVTP)的马尔可夫转换(MS)模型。特别地，我们将Bazzi等人(2017)提出的广义自回归得分(GAS)模型的两体制同方差设定扩展至具有体制特异性均值与方差的一般K体制情形。本研究包含全面的蒙特卡洛模拟，并开发了开源的R包\texttt{multiregimeTVTP}用于数据模拟与参数估计。研究发现：体制均值、方差及转移概率可被可靠恢复，但TVTP驱动系数较难识别。另一发现是，由于联合似然曲面$(\sigma^2,A)$存在脊状结构，GAS得分系数在统计上不可识别。此外，我们发现一步点预测对TVTP误设定具有显著鲁棒性，但滤波体制概率则不然，因此正确设定对于刻画体制动态最为关键，而非短时域预测。对四种期限(1961-2024)美国国债零息收益率变动的实证应用表明：由滞后收益率水平驱动的外生设定在拟合优度上优于常数模型与滞后变动模型，而GAS设定因$\hat{A}$坍缩至零导致模型无法收敛，这反映出模拟中观察到的同一可识别性问题。