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Two questions regarding the equivalence (or lack thereof) of vector error correction model (VECM) cointegrated vector ARMA model (CVARMA) and dynamic factor model (DFM):

  1. Can every VECM CVARMA be expressed in an equivalent DFM representation?
  2. Can every DFM be expressed in an equivalent VECM CVARMA 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:

  1. Is DFM by Pena & Poncela (2006) implemented in any statistical software? Preferably in R?
  2. 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.
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I am not sure whether the answer to the first two questions should be "yes" or "no"; but I have a feeling that VECM CVARMA and DFM are two sides of the same coin:

  • Both in VECM CVARMA and in DFM, the underlying processes are cointegrated; thus there actually are fewer (unobserved) integrated time series components than there are observed endogenous variables.
  • The components are modelled either implicitly (in VECM CVARMA) or explicitly (in DFM).

A special case of CVARMA is the vector error correction model (VECM). With regards to computational advantages, VECM is faster to compute (via OLS or GLS) and is readily available in most statistical/econometric packages. Meanwhile, DFM is slower to compute (it needs fitting a state space model) and apparently not readily available in the statistical/econometric software.

I have not seen DFM by Pena & Poncela (2006) implemented in R.

I do not have an answer regarding computational advantages between CVARMA and DFM.

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