Periodically Correlated Random Sequences
Spectral Theory and Practice
Wiley Series in Probability and Statistics
1. Auflage Oktober 2007
384 Seiten, Hardcover
Wiley & Sons Ltd
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.
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
Abolghassem Miamee, PhD, is Professor of Mathematics at HamptonUniversity in Virginia. His research interests include stochasticprocesses, time series analysis, and harmonic and functionalanalysis.
