马尔可夫切换时变参数自回归模型的贝叶斯推断

Bayesian Inference for Markov-Switching Autoregressive Model with Time-Varying Parameter

摘要: 本文针对马尔可夫切换时变参数自回归模型构建一套完整的贝叶斯推断框架。传统极大似然估计在处理高维时变参数与潜状态转移耦合的问题时，常存在数值不稳定、易陷于局部最优及不确定性量化不足等局限。为应对这些挑战，本研究设计一种高效的马尔可夫链蒙特卡洛抽样算法，整合对数尺度下的隐状态前向滤波–后向抽样、时变系数的卡尔曼平滑，以及基于共轭先验的转移概率吉布斯抽样步骤，并通过引入平稳性先验约束确保动态过程的合理性。模拟实验表明，该算法收敛稳定、估计精度高：主要参数的后验均值相对偏差普遍低于5%，潜在状态路径恢复准确率达100%，样本内拟合效果良好。本研究为同时蕴含结构突变与参数渐进演化特征的时间序列分析提供一个计算可靠、推断完备的贝叶斯解决方案。

Abstract: This paper develops a comprehensive Bayesian inference framework for Markov-switching time-varying parameter autoregressive model. Traditional maximum likelihood estimation often encounters limitations such as numerical instability, a tendency to converge to local optima, and insufficient uncertainty quantification when dealing with high-dimensional time-varying parameters intertwined with latent regime shifts. To address these challenges, this study designs an efficient Markov chain Monte Carlo sampling algorithm that integrates log-scale forward filtering-backward sampling for latent states, Kalman smoothing for time-varying coefficients, and Gibbs sampling steps for transition probabilities based on conjugate priors. Stationarity-inducing prior constraints are also incorporated to ensure the plausibility of the dynamic process. Simulation experiments demonstrate that the proposed algorithm exhibits stable convergence and high estimation accuracy: the relative deviations of posterior means for key parameters are generally below 5%, the recovery accuracy of latent regime paths reaches 100%, and in-sample fitting performance is satisfactory. This research provides a computationally reliable and inferentially complete Bayesian solution for analyzing time series that exhibit both structural breaks and gradual parameter evolution.