[Zurück]

M. Deistler, Brian Anderson, E. Felsenstein, A. Filler, B. Funovits:
"Generalized Linear Factor Models";
Vortrag: Statistical Models for Financial Data III, Graz (eingeladen); 23.05.2012 - 26.05.2012.

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 plaguing
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, as well as the sample
size are going to in¯nity; the decomposition of the observations into these two
components is unique only for n tending to in¯nity.
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. Accord-
ingly the latent variables are modeled as a possibly singular autoregressive process
and (generalized) Yule-Walker equations are used for parameter estimation. The
Yule-Walker equations do not necessarily have a unique solution in the singular
case, and the resulting complexities are examined with a view to ¯nd a stable and
coprime system.
Finally we present some preliminary results for the mixed frequency case,
where the time series components are sampled at di®erent rates. We consider
identi¯ability and estimation from mixed frequency data based on extended Yule-
Walker equations.

http://publik.tuwien.ac.at/files/PubDat_211118.pdf