Periodically Correlated Random Sequences: Spectral Theory and Practice (Wiley Series in Probability and Statistics) - Hardcover

Hurd, Harry L.; Miamee, Abolghassem

Hardcover

ISBN 10: 047134771X ISBN 13: 9780471347712

Publisher: Wiley-Interscience, 2007

Synopsis

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.

About this title

About the Author

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.

From the Back Cover

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

The use of periodically correlated (or cyclostationary) processes has become increasingly popular in a range of research areas such as meteorology, climate, communications, economics, and machine diagnostics. Periodically Correlated Random Sequences presents the main ideas of these processes through the use of basic definitions along with motivating, insightful, and illustrative examples. Extensive coverage of key concepts is provided, including second-order theory, Hilbert spaces, Fourier theory, and the spectral theory of harmonizable sequences. The authors also provide a paradigm for nonparametric time series analysis including tests for the presence of PC structures.

Features of the book include:

• An emphasis on the link between the spectral theory of unitary operators and the correlation structure of PC sequences

• A discussion of the issues relating to nonparametric time series analysis for PC sequences, including estimation of the mean, correlation, and spectrum

• A balanced blend of historical background with modern application-specific references to periodically correlated processes

• An accompanying Web site that features additional exercises as well as data sets and programs written in MATLAB® for performing time series analysis on data that may have a PC structure

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

From the Inside Flap

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

The use of periodically correlated (or cyclostationary) processes has become increasingly popular in a range of research areas such as meteorology, climate, communications, economics, and machine diagnostics. Periodically Correlated Random Sequences presents the main ideas of these processes through the use of basic definitions along with motivating, insightful, and illustrative examples. Extensive coverage of key concepts is provided, including second-order theory, Hilbert spaces, Fourier theory, and the spectral theory of harmonizable sequences. The authors also provide a paradigm for nonparametric time series analysis including tests for the presence of PC structures.

Features of the book include:

• An emphasis on the link between the spectral theory of unitary operators and the correlation structure of PC sequences

• A discussion of the issues relating to nonparametric time series analysis for PC sequences, including estimation of the mean, correlation, and spectrum

• A balanced blend of historical background with modern application-specific references to periodically correlated processes

• An accompanying Web site that features additional exercises as well as data sets and programs written in MATLAB® for performing time series analysis on data that may have a PC structure

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

Edition details

• Publisher: Wiley-Interscience
• Publication date: 2007
• Language: English
• ISBN 10: 047134771X
• ISBN 13: 9780471347712
• Binding: Hardcover
• Edition number: 1
• Number of pages: 384