Modelling High Dimensional Time Series by Generalized Factor Models

Professor Manfred Deistler (Vienna University of Technology)

SYSTEMS AND CONTROL SERIES

DATE: 2011-11-04
TIME: 11:00:00 - 12:00:00
LOCATION: RSISE Seminar Room, ground floor, building 115, cnr. North and Daley Roads, ANU
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ABSTRACT:
We consider generalized linear dynamic factor models. These models have been developed recently and they are used for forecasting and analysis of high dimensional time series in order to overcome the curse of dimensionality plagueing traditional multivariate time series analysis.

We consider a stationary framework; the observations are represented as the sum of two uncorrelated component processes: The so called latent process, which is obtained from a dynamic linear transformation of a low dimensional factor process and which shows strong dependence of its components, and the noise process, which shows weak dependence of the components. The latent process is assumed to have a singular rational spectral density. For the analysis, the cross sectional dimension N, i.e. the number of single time series is going to infinity; the decomposition of the observations into these two components is unique only for N tending to infinity.

We present a structure theory giving a state space or ARMA realization for the latent process, commencing from the second moments of the observations. The emphasis is on the zeroless case, which is generic in the setting considered. Accordingly the latent variables are modeled as a singular autoregressive process and (generalized) YuleWalker equations are used for parameter estimation. The YuleWalker equations do not necessarily have a unique solution in the singular case, and the resulting complexities are examined with a view to find a stable and coprime system.

BIO:
Manfred Deistler was born in Austria. He received his Dipl. Ing. degree in Electrical Engineering from Vienna University of Technology in 1964, and his doctoral degree (Dr. tech.) in Applied Mathematics from the same university in 1970. He was Associate Professor of Statistics at Bonn University from 1973 till 1978, and was then appointed to Full Professor at the Department of Mathematics at Vienna University of Technology, where he still remains. His research interests include time series analysis, systems identification and econometrics. He is a Fellow of the Econometric Society, IEEE and of the Journal of Econometrics.