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The Statistical Theory of Linear SystemsThe Statistical Theory of Linear Systems

E. J. Hannan and Manfred Deistler

Classics in Applied Mathematics 70

Originally published in 1988, The Statistical Theory of Linear Systems deals with identification (in the sense of obtaining a model from data) of multi-input and multi-output linear systems, in particular systems in ARMAX and state space form.

The book emphasizes the underlying theory. It covers
• structure theory, in particular realization and parameterization of linear systems, with special emphasis on the analysis of properties of parameter spaces and parameterizations relevant for estimation and model selection;
• Gaussian maximum likelihood estimation of the real-valued parameters of linear systems, with an emphasis on asymptotic theory;
• model selection, in particular order estimation, by information criteria such as AIC or BIC, with an emphasis on asymptotic theory;
• procedures for calculation of estimates; and
• approximation by rational functions.

This edition includes an extensive new introduction that outlines central ideas and features of the subject matter, as well as developments since the book’s original publication, such as subspace identification, data-driven local coordinates, and the results on post-model-selection estimators. It also provides a section of errata and an updated bibliography.

Researchers and graduate students studying time series statistics, systems identification, econometrics, and signal processing will find this book useful for its comprehensive theoretical analysis and, in particular, for its interweaving of foundational information on structure theory and statistical analysis of linear systems.

E. J. Hannan (1921-1994) was Professor of Statistics at the Australian National University in Canberra. He was a pioneer of modern time series analysis and winner of both the Pitman Medal and the Thomas Ranken Lyle Medal. The Australian Academy of Sciences commemorates his work by awarding the Hannan Medal every two years to recognize achievements of Australians in pure mathematics, applied and computational mathematics, and statistical science.

Manfred Deistler is Emeritus Professor at the Vienna University of Technology and a member of the visiting faculty of the Institute of Advanced Studies, Vienna. He is a Fellow of the Econometric Society, the IEEE, and the Journal of Econometrics.

Preface to the Classics Edition;
Introduction to the Classics Edition;
Index of Notations;
Chapter 1: Linear Systems and Stationary Processes;
Chapter 2: Realization and Parameterization of Linear Dynamic Systems;
Chapter 3: The Kalman Filter;
Chapter 4: Maximum Likelihood Estimation of Armax Systems;
Chapter 5: Estimating the Order of a Linear System;
Chapter 6: Calculation of the Estimates;
Chapter 7: Approximation by Rational Transfer Functions;
Author Index;
Subject Index.

To request an examination copy or desk copy of this book, please use our online request form at

ARMA(X) and state-space systems, time series analysis, system identification, parameterization of linear systems, maximum likelihood estimation

2012 / xlvi + 380 / Softcover / ISBN 978-1-611972-18-4
List Price $99.00 / SIAM Member Price $69.30 / Order Code CL70
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