Time series: data analysis and theory

David R. Brillinger9780898715019, 0898715016

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 higher-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.
Audience 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.

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Table of contents :
Time Series Data Analysis and Theory……Page 1
CONTENTS……Page 10
PREFACE TO THE CLASSICS EDITION……Page 14
PREFACE TO THE EXPANDED EDITION……Page 18
PREFACE TO THE FIRST EDITION……Page 20
1 THE NATURE OF TIME SERIES AND THEIR FREQUENCY ANALYSIS……Page 22
2 FOUNDATIONS……Page 37
3 ANALYTIC PROPERTIES OF FOURIER TRANSFORMS AND COMPLEX MATRICES……Page 70
4 STOCHASTIC PROPERTIES OF FINITE FOURIER TRANSFORMS……Page 109
5 THE ESTIMATION OF POWER SPECTRA……Page 137
6 ANALYSIS OF A LINEAR TIME INVARIANT RELATION BETWEEN A STOCHASTIC SERIES AND SEVERAL DETERMINISTIC SERIES……Page 207
7 ESTIMATING THE SECOND-ORDER SPECTRA OF VECTOR-VALUED SERIES……Page 253
8 ANALYSIS OF A LINEAR TIME INVARIANT RELATION BETWEEN TWO VECTOR-VALUED STOCHASTIC SERIES……Page 307
9 PRINCIPAL COMPONENTS IN THE FREQUENCY DOMAIN……Page 358
10 THE CANONICAL ANALYSIS OF TIME SERIES……Page 388
PROOFS OF THEOREMS……Page 413
REFERENCES……Page 482
NOTATION INDEX……Page 509
AUTHOR INDEX……Page 511
SUBJECT INDEX……Page 517
ADDENDUM Fourier Analysis of Stationary Processes……Page 522