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M. Zamani:
"Modeling multivariable time series using regular and singular autoregressions";
Betreuer/in(nen), Begutachter/in(nen): Brian Anderson, M. Deistler; ANU Canberra, 2014.

The primary aim of this thesis is to study the modeling of high-dimensional time
series with periodic missing observations. This study is very important in different
branches of science and technology such as: econometric modeling, signal processing
and systems and control. For instance, in the field of econometric modeling, it is
crucial to provide proper models for national economies to help policy makers with
decision making and policy adjustments. These models are built upon available highdimensional
data sets, which are not usually collected at the same rate. For example,
some data such as, the employment rate are available on a monthly basis while some
others like the gross domestic product (GDP) are collected quarterly. Motivated by
applications in econometric modeling, we mainly consider systems, which have two
sets of measurement streams, one stream being available at all times and the other
one is observed every N-th time.
There are two major issues involved with modeling of high-dimensional time
series with periodic missing observations, namely, the curse of dimensionality and
missing observations. Generalized dynamic factor models (GDFMs), which have
been recently introduced in the field of econometric modeling, are exploited to handle
the curse of dimensionality phenomenon. Furthermore, the blocking technique
from systems and control is used to tackle issues associated with the missing observations.
In this thesis, we consider a class of GDFMs and assume that there exists an underlying
linear time-invariant system operating at the highest sample rate and our
task is to identify this model from the available mixed frequency measurements. To
this end, we first provide a very detailed study about zeros of linear systems with
alternate missing measurements. Zeros of this class of linear systems are examined
when the parameter matrices A, B, C and D in a minimal state space representation
of a transfer function matrix C(zI 􀀀 A)􀀀1B+D corresponding to the underlying high
frequency system assume generic values. Under this setting, we then illustrate situations
under which linear systems with missing observations are completely zero-free.
It is worthwhile noting that the obtained condition is very common in an econometric
modeling context. Then we apply this result and assume that the underlying high
frequency system has an autoregressive (AR) structure. Next, we study identifiability
of AR systems from those population second order moments, which can be observed
in principle. We propose the method of modified extended Yule-Walker equations
to show that the set of identifiable AR systems is an open and dense subset of the
associated parameter space i.e. AR systems are generically identifiable.