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Special Semester on Stochastics with Emphasis on Finance
Linz, September 2008 - December 2008
Tutorial: Manfred Deistler

Title: System Identification General Aspects and Structure.

Abstract: In this lecture we are concerned with system identification, i.e. with data driven modelling. We assume that the data are discrete time and equally spaced time series. The model class consists of systems in the form of difference equations, partly with stochastic inputs.

A good part of the lecture is concerned with identification of linear systems, mainly in ARMAX or state space form. Identification of linear systems is a nonlinear problem and many problems arising in this context, also arise for nonlinear systems.

We consider three modules, namely

(1)Structure Theory: Here we consider the relation between external behavior and internal parameters. We commence from the population moments of the observations and consider problems of identifiability, realization and parametrization

(2)Estimation for a given parametric subclass: The main emphasis here is on maximum likelihood estimation and asymptotic properties, such as consistency and asymptotic normality.

(3)Model selection: Here the emphasis is on information criteria like AIC or BIC

In addition to the linear main stream case, also linear dynamic factor models and cointegration are discussed. Finally a few examples and some aspects of identification of nonlinear systems are presented.

Presentation slides: Tutorial

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