Spectral Analysis for Univariate Time Series
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.
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.
Focuses on practical application of spectral analysis of time series, with examples
from environmental, engineering and physical sciences.