Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts
提出一种贝叶斯方法，将自回归时间序列中的未观测状态视为缺失数据，利用吉布斯采样进行推断，适用于存在均值和方差体制转换的模型，并给出参数、状态、未来观测和残差的后验分布。
We examine autoregressive time series models that are subject to regime switching. These shifts are determined by the outcome of an unobserved two-state indicator variable that follows a Markov process with unknown transition probabilities. A Bayesian framework is developed in which the unobserved states, one for each time point, are treated as missing data and then analyzed via the simulation tool of Gibbs sampling. This method is expedient because the conditional posterior distribution of the parameters, given the states, and the conditional posterior distribution of the states, given the parameters, all have a form amenable to Monte Carlo sampling. The approach is straightforward and generates marginal posterior distributions for all parameters of interest. Posterior distributions of the states, future observations, and the residuals, averaged over the parameter space are also obtained. Several examples with real and artificial data sets and weak prior information illustrate the usefulness of the methodology.