Factor Sequences are stochastic double sequences $(y_{it}: i \in \mathbb N, t \in \mathbb Z)$ indexed in time and cross-section which have a so called factor structure. The name was coined by Forni et al. 2001, who introduced dynamic factor sequences. We show the difference between dynamic factor sequences and static factor sequences which are the most common workhorse model of econometric factor analysis building on Chamberlain and Rothschild (1983), Stock and Watson (2002) and Bai and Ng (2002). The difference consists in what we call the weak common component which is spanned by a potentially infinite number of weak factors. Ignoring the weak common component can have substantial consequences for applications of factor models in structural analysis and forecasting. We also show that the dynamic common component of a dynamic factor sequence is causally subordinated to the output under general conditions. As a consequence only the dynamic common component can be interpreted as the projection on the common structural shocks of the economy whereas the static common component models the contemporaneous co-movement.

翻译：因子序列是同时在时间和横截面维度上索引的随机双序列$(y_{it}: i \in \mathbb N, t \in \mathbb Z)$，具有所谓的因子结构。该术语由Forni等人（2001）提出，他们引入了动态因子序列。我们展示了动态因子序列与静态因子序列之间的差异，后者是基于Chamberlain和Rothschild（1983）、Stock和Watson（2002）以及Bai和Ng（2002）构建的计量经济因子分析中最常用的工作模型。这种差异在于我们所谓的弱共同成分，它由潜在无限数量的弱因子张成。忽略弱共同成分可能对因子模型在结构分析和预测中的应用产生重大影响。我们还证明了，在一般条件下，动态因子序列的动态共同成分在因果关系上从属于输出。因此，只有动态共同成分可以被解释为对经济中共同结构冲击的投影，而静态共同成分则建模同期共同运动。