Two questions regarding the equivalence (or lack thereof) of vector error correction model (VECM) cointegrated vector ARMA model (CVARMA) and dynamic factor model (DFM):
- Can every
VECMCVARMA be expressed in an equivalent DFM representation? - Can every DFM be expressed in an equivalent
VECMCVARMA representation?
I understand "equivalence of representations" as follows: two representations of a model are equivalent if, given the same data inputs, the model outputs for both representations are the same. (Sorry for a sloppy definition.)
A few different models share the same name of DFM. The version I refer to here is the one by Pena & Poncela (2006). My question does not consider any other version of DFM.
I do not necessarily need a highly formal solution; intuitive explanations are welcome!
Two additional questions:
- Is DFM by Pena & Poncela (2006) implemented in any statistical software? Preferably in
R
? - Are there computational advantages to one or the other approach?
References
- Peña, Daniel, and Pilar Poncela. "Nonstationary dynamic factor analysis." Journal of Statistical Planning and Inference 136.4 (2006): 1237-1257.