  Factor Sequences are stochastic double sequences indexed in time and
cross-section which have a so called factor structure. The term was coined by
Forni and Lippi (2001) who introduced dynamic factor sequences. We introduce
the distinction between dynamic- and static factor sequences which has been
overlooked in the literature. Static factor sequences, where the static factors
are modeled by a dynamic system, are the most common model of macro-econometric
factor analysis, building on Chamberlain and Rothschild (1983a); Stock and
Watson (2002a); Bai and Ng (2002).
  We show that there exist two types of common components - a dynamic and a
static common component. The difference between those consists of the weak
common component, which is spanned by (potentially infinitely many) weak
factors. We also show that the dynamic common component of a dynamic factor
sequence is causally subordinated to the output under suitable conditions. As a
consequence only the dynamic common component can be interpreted as the
projection on the infinite past of the common innovations of the economy, i.e.
the part which is dynamically common. On the other hand the static common
component captures only the contemporaneous co-movement.
