Model identification and data analysis

This book is about constructing models from experimental data. It covers a range of topics, from statistical data prediction to Kalman filtering, from black-box model identification to parameter estimation, from spectral analysis to predictive control. Written for graduate students, this textbook offers an approach that has proven successful throughout the many years during which its author has taught these topics at his University. The book: -Contains accessible methods explained step-by-step in simple terms -Offers an essential tool useful in a variety of fields, especially engineering, statistics, and mathematics -Includes an overview on random variables and stationary processes, as well as an introduction to discrete time models and matrix analysis -Incorporates historical commentaries to put into perspective the developments that have brought the discipline to its current state -Provides many examples and solved problems to complement the presentation and facilitate comprehension of the techniques presented.

Cover; Title Page; Copyright; Contents; Introduction; Acknowledgments; Chapter 1 Stationary Processes and Time Series; 1.1 Introduction; 1.2 The Prediction Problem; 1.3 Random Variable; 1.4 Random Vector; 1.4.1 Covariance Coefficient; 1.5 Stationary Process; 1.6 White Process; 1.7 MA Process; 1.8 AR Process; 1.8.1 Study of the AR(1) Process; 1.9 Yule-Walker Equations; 1.9.1 Yule-Walker Equations for the AR(1) Process; 1.9.2 Yule-Walker Equations for the AR(2) and AR(n) Process; 1.10 ARMA Process; 1.11 Spectrum of a Stationary Process; 1.11.1 Spectrum Properties

1.11.1.0 Proof of the Spectrum Properties1.11.2 Spectral Diagram; 1.11.3 Maximum Frequency in Discrete Time; 1.11.4 White Noise Spectrum; 1.11.5 Complex Spectrum; 1.12 ARMA Model: Stability Test and Variance Computation; 1.12.1 Ruzicka Stability Criterion; 1.12.2 Variance of an ARMA Process; 1.13 Fundamental Theorem of Spectral Analysis; 1.14 Spectrum Drawing; 1.15 Proof of the Fundamental Theorem of Spectral Analysis; 1.16 Representations of a Stationary Process; Chapter 2 Estimation of Process Characteristics; 2.1 Introduction; 2.2 General Properties of the Covariance Function

2.3 Covariance Function of ARMA Processes2.…