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Abstract for "Generalized Linear Dynamic Factor Models-An Approach via Singular Auroregressions" by Manfred Deistler
We consider generalized linear dynamic factor models. These models have been developed for modelling and forecasting high dimensional time series in order to overcome the “curse of dimensionality”. We present a structure (or representation-) theory, where the latent variables and the static factors are represented by state-space or ARMA systems. Emphasis is laid on the case where the transfer functions of such systems are zeroless . This case is shown to be generic in the setting considered. In the zeroless case the latent variables as well as the static factors are modelled as a possibly singular autoregressive processes (i.e. the variance matrix of the one step ahead forecasts may be singular). Based on this structure theory (generalized) Yule Walker equations are used for parameter estimation. In addition model selection -in particular estimation of the dimension of the dynamic factors, the static factors and the states- is discussed.