Molenaar Peter C M
a The Pennsylvania State University.
Multivariate Behav Res. 2017 Mar-Apr;52(2):242-258. doi: 10.1080/00273171.2016.1277681. Epub 2017 Feb 16.
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.
动态因子模型和自回归模型。结果表明，探索性动态因子模型可以进行旋转，对于任何观测序列都会产生一组无穷的等价解。还表明，具有滞后因子载荷的动态因子模型与当前流行的状态空间模型不等价，并且将注意力限制在后一种模型类型可能会产生无效结果。已知的等价向量自回归模型类型，即标准型和结构型，被赋予了一种新的解释，在这种解释中，它们被视为一种创新型混合向量自回归模型的极端情况。结果表明，考虑混合模型可以解决许多问题，特别是在格兰杰因果关系检验方面。
