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Time Series: Data Analysis and TheoryTime Series: Data Analysis and Theory

David R. Brillinger

Classics in Applied Mathematics 36

Intended for students and researchers, this text employs basic techniques of univariate and multivariate statistics for the analysis of time series and signals. It provides a broad collection of theorems, placing the techniques on firm theoretical ground. The techniques, which are illustrated by data analyses, are discussed in both a heuristic and a formal manner, making the book useful for both the applied and the theoretical worker. An extensive set of original exercises is included.

Time Series: Data Analysis and Theory takes the Fourier transform of a stretch of time series data as the basic quantity to work with and shows the power of that approach. It considers second- and higherr-order parameters and estimates them equally, thereby handling non-Gaussian series and nonlinear systems directly. The included proofs, which are generally short, are based on cumulants.


This book will be most useful to applied mathematicians, communication engineers, signal processors, statisticians, and time series researchers, both applied and theoretical. Readers should have some background in complex function theory and matrix algebra and should have successfully completed the equivalent of an upper division course in statistics.


Preface to the Classics Edition; Preface to the Expanded Edition; Preface to the First Edition; Chapter 1: The Nature of Time Series and Their Frequency Analysis; Chapter 2: Foundations; Chapter 3: Analytic Properties of Fourier Transforms and Complex Matrices; Chapter 4: Stochastic Properties of Finite Fourier Transforms; Chapter 5: The Estimation of Power Spectra; Chapter 6: Analysis of a Linear Time Invariant Relation Between a Stochastic Series and Several Deterministic Series; Chapter 7: Estimating the Second-Order Spectra of Vector-Valued Series; Chapter 8: Analysis of a Linear Time Invariant Relation Between Two Vector-Valued Stochastic Series; Chapter 9: Principal Components in the Frequency Domain; Chapter 10: The Canonical Analysis of Time Series; Proofs of Theorems; References; Notation Index; Author Index; Subject Index; Addendum: Fourier Analysis of Stationary Processes

2001 / xx + 540 pages / Softcover / ISBN-13: 978-0-898715-01-9 / ISBN-10: 0-89871-501-6 /
List Price $82.50 / SIAM Member Price $57.75 / Order Code CL36
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