Studying co-movements in large multivariate data prior to multivariate modelling

A characterization of vector autoregressive processes with common cyclical features

“…Using this notation, we introduce the final equations (FE) Zellner and Palm (1974), Cubadda, Hecq, and Palm (2009); eliminating the common factors as in Lemma 2.1 one obtains…”

“…Some implications of the existence results are the following. Cubadda, Hecq, and Palm (2009) showed that CS implies CE; the existence results also give the reverse implication, i.e. that CE implies CS.…”

“…Kugler and Neusser (1993), Lippi and Reichlin (1994), Vahid and Issler (2002), Urbain (2002, 2006), Paruolo (2003Paruolo ( , 2006, Schleicher (2007) and Cubadda, Hecq, and Palm (2009).…”

“…Yet another form of common dynamics requires common factors in the set of final equations (FE), see eq. (2.7) in Zellner and Palm (1974) and Cubadda, Hecq, and Palm (2009); we refer to this notion as CE(d), where d refers to the degree of the MA polynomial in the FE of the CE linear combination.…”

“…Finally Cubadda, Hecq, and Palm (2009) considered the implications of CS and CI on the FE representation of VAR processes, en route to obtain the orders of the univariate ARMA(p, q) representations of single component time series. In particular they derived the implications of CS(d) on p, q for d ≥ 0, both for stationary and CI VAR processes with I(1) variables.…”