Periodically Correlated Random Sequences

Spectral Theory and Practice
1. Auflage 2007
ISBN: 978-0-471-34771-2
Verlag: Wiley

Buch, Englisch, 384 Seiten, Format (B × H): 161 mm x 242 mm, Gewicht: 658 g

Uniquely combining theory, application, and computing, this bookexplores the spectral approach to time series analysis

The use of periodically correlated (or cyclostationary)processes has become increasingly popular in a range of researchareas such as meteorology, climate, communications, economics, andmachine diagnostics. Periodically Correlated Random Sequencespresents the main ideas of these processes through the use of basicdefinitions along with motivating, insightful, and illustrativeexamples. Extensive coverage of key concepts is provided, includingsecond-order theory, Hilbert spaces, Fourier theory, and thespectral theory of harmonizable sequences. The authors also providea paradigm for nonparametric time series analysis including testsfor the presence of PC structures.

Features of the book include:

* An emphasis on the link between the spectral theory of unitaryoperators and the correlation structure of PC sequences
* A discussion of the issues relating to nonparametric time seriesanalysis for PC sequences, including estimation of the mean,correlation, and spectrum
* A balanced blend of historical background with modernapplication-specific references to periodically correlatedprocesses
* An accompanying Web site that features additional exercises aswell as data sets and programs written in MATLAB® forperforming time series analysis on data that may have a PCstructure

Periodically Correlated Random Sequences is an ideal text ontime series analysis for graduate-level statistics and engineeringstudents who have previous experience in second-order stochasticprocesses (Hilbert space), vector spaces, random processes, andprobability. This book also serves as a valuable reference forresearch statisticians and practitioners in areas of probabilityand statistics such as time series analysis, stochastic processes,and prediction theory.

Autoren/Hrsg.

Hurd, Harry L

Miamee, Abolghassem

Inhaltsverzeichnis

Preface xiii

Acknowledgments xv

Glossary xvii

1 Introduction

2 Examples, Models, and Simulations 19

3 Review of Hilbert Spaces 45

4 Stationary Random Sequences 67

5 Harmonizable Sequence 133

6 Fourier Theory of the Covariance 151

7 Representations of PC Sequences 199

8 Prediction of Sequences 215

9 Estimation of Mean and Covariance 249

10 Spectral Estimation 297

11 A Paradigm for Nonparametric Analysis of PC Time Series 331

References 337

Index 351

Über Autor(innen)

Harry L. Hurd, PhD, is Adjunct Professor of Statistics at TheUniversity of North Carolina at Chapel Hill. He is the founder ofHurd Associates, Inc., a research and development firmconcentrating in the areas of signal processing and stochasticprocesses. Dr. Hurd has published extensively on the topics ofnonstationary random processes, periodically correlated processes,and nonparametric time series.

Abolghassem Miamee, PhD, is Professor of Mathematics at HamptonUniversity in Virginia. His research interests include stochasticprocesses, time series analysis, and harmonic and functionalanalysis.