Equivalent Dynamic Models

Equivalences of two classes of dynamic models for weakly stationary multivariate time series are discussed: dynamic factor models and autoregressive models. It is shown that exploratory dynamic factor models can be rotated, yielding an infinite set of equivalent solutions for any observed series. It also is shown that dynamic factor models with lagged factor loadings are not equivalent to the currently popular state-space models, and that restriction of attention to the latter type of models may yield invalid results. The known equivalent vector autoregressive model types, standard and structural, are given a new interpretation in which they are conceived of as the extremes of an innovating type of hybrid vector autoregressive models. It is shown that consideration of hybrid models solves many problems, in particular with Granger causality testing.

本文针对弱平稳多元时间序列，探讨了两类动态模型的等价性：动态因子模型（dynamic factor models）与自回归模型。研究发现，探索性动态因子模型可通过旋转操作，为任意观测序列生成无穷多组等价解。此外，研究证实，带有滞后因子载荷的动态因子模型与当前主流的状态空间模型（state-space models）并不等价；若仅将分析局限于这类状态空间模型，可能会得到无效的结论。针对现有两类等价向量自回归模型（vector autoregressive model）——标准型与结构型，本文给出了全新的解读框架：将其视作一类创新型混合向量自回归模型的两个极端场景。研究表明，引入混合向量自回归模型可解决诸多分析难题，尤其是在格兰杰因果检验（Granger causality testing）场景中。