VARMA Models with Single- or Mixed-Frequency Data: New Conditions for Extended Yule–Walker Identification

Abstract

This paper deals with the identifiability of VARMA models with VAR order greater than or equal to the MA order, in the context of mixed-frequency data (MFD) using extended Yule–Walker equations. The main contribution is that necessary and sufficient conditions for identifiability in the single-frequency data case are expressed in an original way and yield new results in the MFD case. We also provide two counterexamples that answer an open question in this topic about whether certain sufficient conditions are necessary for identifiability. Therefore, this paper expands the set of models that can be identified with MFD using extended Yule–Walker equations. The main idea is that with MFD, some autocovariance blocks are not available from observed variables and, in some cases, the new conditions in this paper can be used to reconstruct all the non-available covariance blocks from available covariance blocks.