Title: High frequency linear time series models and mixed frequency data
Authors: Manfred Deistler - Vienna University of Technology (Austria) [presenting]
Abstract: The focus is on the identifiability of the parameters of high frequency multivariate ARMA type models from mixed frequency time series data. For the VAR case, we demonstrate identifiability for generic parameter values using the population second moments of the observations. We display a constructive algorithm for the parameter values and establish the continuity of the mapping attaching the high frequency parameters to these populations second moments. These structural results are obtained using two alternative tools: extended Yule Walker equations and blocking of the output process. The cases of stock and flow variables, as well as of general linear transformations of high frequency data, are treated. We discuss how our constructive identifiability results can be used for parameter estimation. In a next step we show that the results on generic identifiability can be extended to the VARMA case, provided that the MA order is smaller than or equal to the AR order. However, in the case where the MA order exceeds the AR order, and in particular in the VMA case, results are completely different. Then, when the innovation covariance matrix is non-singular, ``typically'' non-identifiability occurs not even local identifiability. This is because, e.g., in the VMA case, as opposed to the VAR case, the not directly observed auto-covariances of the output can vary ``freely''.Finally, we discuss modeling by generalized linear dynamic factor models in the mixed frequency case.