[Zurück]

M. Deistler:
"Modeling High Dimensional Time Series by Generalized Factor Models";
Hauptvortrag: 19th International Symposium on Mathematical Theory of Network and Systems, Budapest., Ungarn (eingeladen); 05.07.2010 - 09.07.2010; in: "Proceedings of the MTNS", Proceedings of the 19th Int. Symposium on MTNS (2010), ISBN: 978-963-311-370-7; S. 323 - 329.

We discuss and analyze generalized linear
dynamic factor models. These models have been developed
recently and they are used to model high dimensional time
series in order to overcome the "curse of dimensionality". The
basic idea in factor models is to seperate "comovement"
between the variables (caused by a relatively small number of
factors) from individual (idiosyncratic) variation. Here factor
analysis is considered in a time series context, where
concentration of information is performed in the crosssectional
and in the time dimension. The models considered are
linear dynamic in nature and stationarity of the processes is
assumed. As opposed to the classical case, in the generalized
case considered here, a certain form of weak dependence of the
noise components is permitted. In the core part of the paper,
we are concerned with structure theory, namely with realizing
the singular rational spectral density of the latent variables by
a linear system. Special emphasis ! is laid on the autoregressive
case, which is generic in our setting. These autoregressions may
have a singular innovation variance, which may cause multiple
solutions for the Yule Walker equations. Finally, identification
procedures, using a suitable denoising procedure and
estimators suggested by our structure theory, are discussed.