Generalized Dynamic Factor Models - The Single and the Mixed Frequency Case

The proposed research project deals with data-driven modelling of Generalized Linear Dynamic Factor Models (GDFM). Such models are used in particular to analyze and forecast high-dimensional time series. The importance of this area has increased considerably over the last decade. Our approach to this problem is based on system theory and its methods. The project consists in the following parts: Single Frequency: We want to further extend our previous results obtained for the AR case. However, our emphasis will be on the more general ARMA case. Structure theory: The focus will be on the ARMA case, in particular on the development of a canonical form for ARMA systems which gives an AR representation whenever the process is AR. Moreover, it is intended to investigate the topological and geometric properties of parameter spaces and parameterizations. Estimation of (real-valued) AR and ARMA parameters: Emphasis is laid on the singular ARMA case for which naive (Gaussian) maximum-likelihood estimation is not possible. The Hannan-Rissanen procedure and appropriate modifications as well as the use of subspace procedures will be considered. Model Selection: Here we consider LASSO type estimation. Mixed Frequency: In many cases, in particular for high-dimensional time series, observations are available at different sampling frequencies. Our aim is to estimate the parameters of the system generating all data at the highest frequency from the mixed frequency data and to use this system for prediction, filtering and smoothing. Accordingly, a central issue will be to develop criteria for identifiability. If such a system is not identifiable from the mixed frequency data, we plan to develop alternative procedures for prediction, filtering and smoothing. Our idea is to work with so-called blocked systems. The estimation procedures developed for the single and mixed frequency case will be tested on real data too.

The project has been concerned with the analysis of multivariate and in particular high dimensional time series, with a special emphasis on the case of mixed frequency (MF) data (i.e. the case where the univariate time series are available at different sampling frequencies). The central parts of the project are concerned with questions of identifiability and with estimation algorithms and their properties, for linear dynamic time series models, taking also into account generalized dynamic factor models (GDFMs), for the mixed frequency case. The topic of the project is of substantial importance for modern macro-econometrics, in the sense that it provides foundations for the analysis of multivariate and in particular high dimensional time series, in the case of mixed frequency observations. This mixed frequency case is very common in economic time series as e.g. financial data are often sampled with higher frequency than typical real macro data. This project has been a continuation of the previous FWF-Project P20833-N18.