Ulteriori informazioni
This book focuses on the methods and theory for the statistical analysis of time series with mixed spectra. It presents detailed theoretical and empirical analyses of important methods and algorithms. Using both simulated and real-world data to illustrate the analyses, the book discusses periodogram analysis, autoregression, maximum likelihood, and covariance analysis. It considers real- and complex-valued time series, with and without the Gaussian assumption. The author also includes the most recent results on the Laplace and quantile periodograms as extensions of the traditional periodogram.
Sommario
Introduction. Basic Concepts. Cramér-Rao Lower Bound. Autocovariance Function. Linear Regression Analysis. Fourier Analysis Approach. Estimation of Noise Spectrum. Maximum Likelihood Approach. Autoregressive Approach. Covariance Analysis Approach. Further Topics. Appendix. Bibliography.
Info autore
Ta-Hsin Li is a research statistician at the IBM Watson Research Center. He was previously a faculty member at Texas A&M University and the University of California, Santa Barbara. Dr. Li is a fellow of the American Statistical Association and an elected senior member of the Institute of Electrical and Electronic Engineers. He is an associate editor for the EURASIP Journal on Advances in Signal Processing, the Journal of Statistical Theory and Practice, and Technometrics. He received a Ph.D. in applied mathematics from the University of Maryland.
Riassunto
Time series with mixed spectra are characterized by hidden periodic components buried in random noise. Despite strong interest in the statistical and signal processing communities, no book offers a comprehensive and up-to-date treatment of the subject. Filling this void, Time Series with Mixed Spectra focuses on the methods and theory for the statistical analysis of time series with mixed spectra. It presents detailed theoretical and empirical analyses of important methods and algorithms.
Using both simulated and real-world data to illustrate the analyses, the book discusses periodogram analysis, autoregression, maximum likelihood, and covariance analysis. It considers real- and complex-valued time series, with and without the Gaussian assumption. The author also includes the most recent results on the Laplace and quantile periodograms as extensions of the traditional periodogram.
Complete in breadth and depth, this book explains how to perform the spectral analysis of time series data to detect and estimate the hidden periodicities represented by the sinusoidal functions. The book not only extends results from the existing literature but also contains original material, including the asymptotic theory for closely spaced frequencies and the proof of asymptotic normality of the nonlinear least-absolute-deviations frequency estimator.
Testo aggiuntivo
"It masterfully integrates the most significant advances in the literature."—Journal of the American Statistical Association
"… an excellent introduction and overview of the literature dealing with statistical inference on time-series involving sinusoids. It will be an indispensable reference that research workers and graduate students of allied fields will rely on in the future."—Mathematical Reviews, January 2015
"It is extremely thorough in its approach. Every term is carefully defined, and many proofs are given in elaborate detail. … The range of problems and methods considered in the book is extensive."—Journal of Time Series Analysis, 2015
