The Statistical Theory of Linear Systems

Originally published in 1988, this classic text treats the identification of noisy (multi-input and multi-output) linear systems, particularly systems in ARMAX and state space form. The book covers structure theory, including identifiability, realisation and parameterisation of linear systems; analysis of topological and geometrical properties of parameter spaces and parameterisations for estimation and model selection; Gaussian maximum likelihood estimation of real-valued parameters of linear systems; model selection; calculation of estimates; and approximation by rational transfer functions. This edition includes an extensive new introduction that outlines 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 interweaving of foundational information on structure theory and statistical analysis of linear systems.