Mixed frequency structured AR model identification

This paper is concerned with identifiability of an underlying high frequency multivariate stable singular AR system from mixed frequency observations. Such problems arise for instance in economics when some variables are observed monthly whereas others are observed quarterly. In particular, this paper studies stable singular AR systems where the covariance matrix associated with the vector obtained by stacking observation vector, y_t, and its lags from the first lag to the p-th one (p is the order of the AR system), is also singular. To deal with this, it is assumed that the column degrees of the associated polynomial matrix are known. We consider first that there are given nonzero unequal column degrees and we show generic identifiability of the system and noise parameters. Then we extend the results to allow zero column degrees corresponding to fast components. In this case, we first show generic identifiability of the subsystem of the components with nonzero column degree. Then we show how to obtain those components of the parameter matrices of the components corresponding to zero column degree by regression.