Parsimonious Parameterization of Vector Autoregressive Moving Average Models
讨论两种方法，用于在模型设定阶段揭示向量ARMA模型的简化结构，从而减少待估参数、实现参数化简约，降低建模复杂度。
It is not uncommon to hear the complaint that there are many difficulties in building vector autoregressive moving average (ARMA) models, such as too many parameters in a model. In this article, I show that the complaint can be avoided if a proper method is used at the model-specification stage to obtain the detailed structure of the vector process under study. Two such methods, one from the engineering literature and the other from the statistical literature, are discussed. The beauty of these methods is that they can reveal the simplifying structure of a vector ARMA model and hence achieve parsimony in parameterization. More specifically, the simplifying structure can identify those parameters that require estimation and those that can be set to 0. The methods discussed, therefore, can substantially reduce the complexity involved in vector time series modeling. I also compare the two methods and suggest modifications of some model-specification statistics available in the literature. An example is given.