In this paper, we propose an effective Bayesian subset selection method for the double-threshold-variable autoregressive moving-average (DT-ARMA) models. The usual complexity of estimation is increased mainly by capturing the correlation between two threshold variables and including moving-average terms in the model. By adopting the stochastic search variable selection method, combined with the Gibbs sampler and Metropolis-Hastings algorithm, we can simultaneously estimate the unknown parameters and select the best subset model from a large number of possible models. The simulation experiments illustrate that the proposed approach performs well. In applications, two real data sets are analyzed by the proposed method, and the fitted DT-ARMA model is better than the double-threshold autoregressive (DT-AR) model from the view of parsimony.

在本文中，我们为双阈值变量自回归移动平均 (DT-ARMA) 模型提出了一种有效的贝叶斯子集选择方法。通常的估计复杂性主要是通过捕获两个阈值变量之间的相关性并在模型中包括移动平均项来增加的。通过采用随机搜索变量选择方法，结合Gibbs采样器和Metropolis-Hastings算法，我们可以同时估计未知参数并从大量可能的模型中选择最佳子集模型。仿真实验表明所提出的方法性能良好。在应用中，本文提出的方法对两个真实数据集进行了分析，拟合后的DT-ARMA模型从简约的角度来看优于双阈值自回归（DT-AR）模型。