Abstract

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:

v  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.

Ø  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.

Ø  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.

Ø  Model Selection: Here we consider LASSO type estimation.

v  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.