The multivariate smooth transition autoregressive model with order k (M‐STAR)(k) is a nonlinear multivariate time series model able to capture regime changes in the conditional mean. The main aim of this paper is to develop a Bayesian estimation scheme for the M‐STAR(k) model that includes the coefficient parameter matrix, transition function parameters, covariance parameter matrix, and the model order k as parameters to estimate. To achieve this aim, the joint posterior distribution of the parameters for the M‐STAR(k) model is derived. The conditional posterior distributions are then shown, followed by the design of a posterior simulator using a combination of Markov chain Monte Carlo (MCMC) algorithms that includes the Metropolis‐Hastings, Gibbs sampler, and reversible jump MCMC algorithms. Following this, extensive simulation studies, as well as case studies, are detailed at the end.

中文翻译：

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多元平滑过渡自回归模型的贝叶斯估计和模型选择

k 阶多元平滑过渡自回归模型 (M-STAR)(k) 是一种非线性多元时间序列模型，能够捕捉条件均值中的状态变化。本文的主要目的是为 M-STAR(k) 模型开发一种贝叶斯估计方案，其中包括系数参数矩阵、转移函数参数、协方差参数矩阵和模型阶数 k 作为参数进行估计。为了实现这一目标，导出了 M-STAR(k) 模型参数的联合后验分布。然后显示条件后验分布，然后使用马尔可夫链蒙特卡罗 (MCMC) 算法的组合设计后验模拟器，其中包括 Metropolis-Hastings、Gibbs 采样器和可逆跳跃 MCMC 算法。在此之后，广泛的模拟研究，