Koopmans / Birnbaum / Lukacs The Spectral Analysis of Time Series

Probability and Mathematical Statistics, Vol. 22
1. Auflage 2014
ISBN: 978-1-4832-1854-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 382 Seiten, Web PDF

The Spectral Analysis of Time Series describes the techniques and theory of the frequency domain analysis of time series. The book discusses the physical processes and the basic features of models of time series. The central feature of all models is the existence of a spectrum by which the time series is decomposed into a linear combination of sines and cosines. The investigator can used Fourier decompositions or other kinds of spectrals in time series analysis. The text explains the Wiener theory of spectral analysis, the spectral representation for weakly stationary stochastic processes, and the real spectral representation. The book also discusses sampling, aliasing, discrete-time models, linear filters that have general properties with applications to continuous-time processes, and the applications of multivariate spectral models. The text describes finite parameter models, the distribution theory of spectral estimates with applications to statistical inference, as well as sampling properties of spectral estimates, experimental design, and spectral computations. The book is intended either as a textbook or for individual reading for one-semester or two-quarter course for students of time series analysis users. It is also suitable for mathematicians or professors of calculus, statistics, and advanced mathematics.

Autoren/Hrsg.

Koopmans, L. H.

Birnbaum, Z. W.

Lukacs, E.

Inhaltsverzeichnis

1;Front Cover;1
2;The Spectral Analysis of Time Series;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Preface;12
7;Acknowledgments;14
8;Chapter 1. Preliminaries;16
8.1;1.1 INTRODUCTION;16
8.2;1.2 TIME SERIES AND SPECTRA;16
8.3;1.3 SUMMARY OF VECTOR SPACE GEOMETRY;28
8.4;1.4 SOME PROBABILITY NOTATIONS AND PROPERTIES;41
9;Chapter 2. Models for Spectral Analysis—The Univariate Case;44
9.1;2.1 INTRODUCTION;44
9.2;2.2 THE WIENER THEORY OF SPECTRAL ANALYSIS;45
9.3;2.3 STATIONARY AND WEAKLY STATIONARY STOCHASTIC PROCESSES;52
9.4;2.4 THE SPECTRAL REPRESENTATION FOR WEAKLY STATIONARY STOCHASTIC PROCESSES—A SPECIAL CASE;54
9.5;2.5 THE GENERAL SPECTRAL REPRESENTATION FOR WEAKLY STATIONARY PROCESSES;56
9.6;2.6 THE DISCRETE AND CONTINUOUS COMPONENTS OF THE PROCESS;61
9.7;2.7 PHYSICAL REALIZATIONS OF THE DIFFERENT KINDS OF SPECTRA;64
9.8;2.8 THE REAL SPECTRAL REPRESENTATION;65
9.9;2.9 ERGODICITY AND THE CONNECTION BETWEEN THE WIENER AND STATIONARY PROCESS THEORIES;68
9.10;2.10 STATISTICAL ESTIMATION OF THE AUTOCOVARIANCE AND THE MEAN ERGODIC THEOREM;70
9.11;APPENDIX TO CHAPTER 2;76
10;Chapter 3. Sampling, Aliasing, and Discrete-Time Models;81
10.1;3.1 INTRODUCTION;81
10.2;3.2 SAMPLING AND THE ALIASING PROBLEM;82
10.3;3.3 THE SPECTRAL MODEL FOR DISCRETE-TIME SERIES;89
11;Chapter 4. Linear Filters—General Properties with Applications to Continuous-Time Processes;94
11.1;4.1 INTRODUCTION;94
11.2;4.2 LINEAR FILTERS;95
11.3;4.3 COMBINING LINEAR FILTERS;111
11.4;4.4 INVERTING LINEAR FILTERS;120
11.5;4.5 NONSTATIONARY PROCESSES GENERATED BY TIME VARYING LINEAR FILTERS;126
11.6;APPENDIX TO CHAPTER 4;129
12;Chapter 5. Multivariate Spectral Models and Their Applications;134
12.1;5.1 INTRODUCTION;134
12.2;5.2 THE SPECTRUM OF A MULTIVARIATE TIME SERIES—WIENER THEORY;136
12.3;5.3 MULTIVARIATE WEAKLY STATIONARY STOCHASTIC PROCESSES;139
12.4;5.4 LINEAR FILTERS FOR MULTIVARIATE TIME SERIES;144
12.5;5.5 THE BIVARIATE SPECTRAL PARAMETERS, THEIR INTERPRETATIONS AND USES;150
12.6;5.6 THE MULTIVARIATE SPECTRAL PARAMETERS, THEIR INTERPRETATIONS AND USES;167
12.7;APPENDIX TO CHAPTER 5;177
13;Chapter 6. Digital Filters;180
13.1;6.1 INTRODUCTION;180
13.2;6.2 GENERAL PROPERTIES OF DIGITAL FILTERS;181
13.3;6.3 THE EFFECT OF FINITE DATA LENGTH;191
13.4;6.4 DIGITAL FILTERS WITH FINITELY MANY NONZERO WEIGHTS;197
13.5;6.5 DIGITAL FILTERS OBTAINED BY COMBINING SIMPLE FILTERS;205
13.6;6.6 FILTERS WITH GAPPED WEIGHTS AND RESULTS CONCERNING THE FILTERING OF SERIES WITH POLYNOMIAL TRENDS;211
13.7;APPENDIX TO CHAPTER 6;220
14;Chapter 7. Finite Parameter Models, Linear Prediction, and Real-Time Filtering;225
14.1;7.1 INTRODUCTION;225
14.2;7.2 MOVING AVERAGES;227
14.3;7.3 AUTOREGRESSIVE PROCESSES;232
14.4;7.4 THE LINEAR PREDICTION PROBLEM;241
14.5;7.5 MIXED AUTOREGRESSIVE–MOVING AVERAGE PROCESSES AND RECURSIVE PREDICTION;255
14.6;7.6 LINEAR FILTERING IN REAL TIME;264
14.7;APPENDIX TO CHAPTER 7;267
15;Chapter 8. The Distribution Theory of Spectral Estimates with Applications to Statistical Inference;272
15.1;8.1 INTRODUCTION;272
15.2;8.2 DISTRIBUTION OF THE FINITE FOURIER TRANSFORM AND THE PERIODOGRAM;273
15.3;8.3 DISTRIBUTION THEORY FOR UNIVARIATE SPECTRAL ESTIMATORS;280
15.4;8.4 DISTRIBUTION THEORY FOR MULTIVARIATE SPECTRAL ESTIMATORS WITH APPLICATIONS TO STATISTICAL INFERENCE;295
15.5;APPENDIX TO CHAPTER 8;306
16;Chapter 9. Sampling Properties of Spectral Estimates, Experimental Design, and Spectral Computations;309
16.1;9.1 INTRODUCTION;309
16.2;9.2 PROPERTIES OF SPECTRAL ESTIMATORS AND THE SELECTION OF SPECTRAL WINDOWS;310
16.3;9.3 EXPERIMENTAL DESIGN;325
16.4;9.4 METHODS FOR COMPUTING SPECTRAL ESTIMATORS;336
16.5;9.5 DATA PROCESSING PROBLEMS AND TECHNIQUES;345
16.6;APPENDIX TO CHAPTER 9;349
17;References;369
18;Index;374