Spectral Analysis for Univariate Time Series: (Series Number 51 Cambridge Series in Statistical and Probabilistic Mathematics)

Spectral analysis is widely used to interpret time series collected in diverse areas. This book covers the statistical theory behind spectral analysis and provides data analysts with the tools needed to transition theory into practice. Actual time series from oceanography, metrology, atmospheric science and other areas are used in running examples throughout, to allow clear comparison of how the various methods address questions of interest. All major nonparametric and parametric spectral analysis techniques are discussed, with emphasis on the multitaper method, both in its original formulation involving Slepian tapers and in a popular alternative using sinusoidal tapers. The authors take a unified approach to quantifying the bandwidth of different nonparametric spectral estimates. An extensive set of exercises allows readers to test their understanding of theory and practical analysis. The time series used as examples and R language code for recreating the analyses of the series are available from the book's website.

Table of Contents:
1. Introduction to spectral analysis; 2. Stationary stochastic processes; 3. Deterministic spectral analysis; 4. Foundations for stochastic spectral analysis; 5. Linear time-invariant filters; 6. Periodogram and other direct spectral estimators; 7. Lag window estimators; 8. Combining direct spectral estimators; 9. Parametric spectral estimators; 10. Harmonic analysis; 11. Simulation of time series.

About the Author :
Donald B. Percival is the author of 75 publications in refereed journals on a variety of topics, including analysis of environmental time series, characterization of instability of atomic clocks and forecasting inundation of coastal communities due to trans-oceanic tsunamis. He is the co-author (with Andrew Walden) of Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques (Cambridge, 1993) and Wavelet Methods for Time Series Analysis (Cambridge, 2000). He has taught graduate-level courses on time series analysis, spectral analysis and wavelets for over thirty years at the University of Washington. Andrew T. Walden has authored 100 refereed papers in scientific areas including statistics, signal processing, geophysics, astrophysics and neuroscience, with an emphasis on spectral analysis and time series methodology. He worked in geophysical exploration research before joining Imperial College London. He is co-author (with Donald B. Percival) of Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques (Cambridge,1993) and Wavelet Methods for Time Series Analysis (Cambridge, 2000). He has taught many courses including time series, spectral analysis, geophysical data analysis, applied probability and graphical modelling, primarily at Imperial College London, and also at the University of Washington.

Review :
'Percival and Walden have written an excellent text for anyone who analyzes or wants to learn how to analyze time series data in the frequency domain. The aims and scope of the text are broad and require the skills that one would acquire in a basic course on mathematical statistics. The authors take a data analysis approach and relegate theoretical material to special sections or problems, and give ample references to the more theoretical details. The authors give philosophical as well as practical guidance in applying spectral techniques to time series data. This book is one of the best texts on the topic and would be useful as a reference for researchers. In addition, the book would be great as a textbook for a one semester/quarter course on the spectral analysis of time series.' David Stoffer, University of Pittsburgh 'I used Spectral Analysis for Physical Applications several times for my spectral analysis courses. It was an excellent addition to the literature. This new book, considerably enlarged, will certainly have the same impact. The authors should be congratulated for a most valuable book.' Pedro A. Morettin, Universidade de São Paulo 'Spectral Analysis for Univariate Time Series is an excellent step-by-step introduction to using Fourier methods in the statistical analysis of time series. The in-depth material, extensive exercises, practical advice, and illustrative data analyses provide valuable insights to readers of varied backgrounds.' Peter F. Craigmile, Ohio State University 'This book will serve scientists and engineers in many fields with a general toolbox for spectral analysis. The fundamentals of non-parametric and parametric methods are presented, together with convincing examples and exercises. I especially appreciate the extensive chapter on combining direct spectral estimators, as todays standard toolbox definitely should include multitaper based spectral analysis.' Maria Sandsten, Lunds universitet 'The book constitutes a lot more than an update of the authors' 1993 book Spectral Analysis for Physical Applications. The stand-out features are still the examples and exercises, but all data analysis has been done in R and considerable effort has gone into explanation, and how the methods fit in with alternatives. There is also a new chapter on simulation. The book is suitable not just as a reference for statisticians, engineers and physicists, but also as a graduate level text, particularly because of the chapter summaries and the thought-provoking comments at the section ends.' Barry Quinn, Macquarie University, Sydney 'The excellent new textbook by Percival and Walden is an important source of information for anyone interested in time series analysis. Theoretical rigour combined with practical analysis of interesting real world data gives the reader a pedagogical journey into the world of spectral analysis and time series analysis. Highly recommended!' Alfred Hanssen, Universitetet i Tromsø – Norges arktiske universitet