A regime-switching multivariate time series model which is closed under margins is built. The model imposes a restriction on all lower-dimensional sub-processes to follow a regime-switching process sharing the same latent regime sequence and having the same Markov order as the original process. The margin-closed regime-switching model is constructed by considering the multivariate margin-closed Gaussian VAR($k$) dependence as a copula within each regime, and builds dependence between observations in different regimes by requiring the first observation in the new regime to depend on the last observation in the previous regime. The property of closure under margins allows inference on the latent regimes based on lower-dimensional selected sub-processes and estimation of univariate parameters from univariate sub-processes, and enables the use of multi-stage estimation procedure for the model. The parsimonious dependence structure of the model also avoids a large number of parameters under the regime-switching setting. The proposed model is applied to a macroeconomic data set to infer the latent business cycle and compared with the relevant benchmark.

翻译：本文构建了一种在边际下闭合的体制转换多元时间序列模型。该模型对所有低维子过程施加约束，使其遵循与原始过程共享相同潜在体制序列且具有相同马尔可夫阶数的体制转换过程。通过将每个体制内的多元边际闭合高斯VAR(k）依赖结构视为一个连接函数(copula），并允许新体制的第一个观测依赖于前一个体制的最后一个观测，从而构建了不同体制间观测值的依赖关系。边际闭合性质允许基于选定的低维子过程对潜在体制进行推断，并可通过单变量子过程估计单变量参数，进而支持模型的多阶段估计流程。该模型简洁的依赖结构也避免了体制转换设定下参数数量过多的问题。将所提模型应用于宏观经济数据集以推断潜在商业周期，并与相关基准模型进行了比较。