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The Spectral Analysis of Time Series

2014-05-12 Mathematics
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Release : 2014-05-12
Genre : Mathematics
Kind : eBook
Book Rating : 546/5 ( reviews)

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Book Synopsis The Spectral Analysis of Time Series by : L. H. Koopmans

Download or read book The Spectral Analysis of Time Series written by L. H. Koopmans. This book was released on 2014-05-12. Available in PDF, EPUB and Kindle. Book excerpt: The Spectral Analysis of Time Series describes the techniques and theory of the frequency domain analysis of time series. The book discusses the physical processes and the basic features of models of time series. The central feature of all models is the existence of a spectrum by which the time series is decomposed into a linear combination of sines and cosines. The investigator can used Fourier decompositions or other kinds of spectrals in time series analysis. The text explains the Wiener theory of spectral analysis, the spectral representation for weakly stationary stochastic processes, and the real spectral representation. The book also discusses sampling, aliasing, discrete-time models, linear filters that have general properties with applications to continuous-time processes, and the applications of multivariate spectral models. The text describes finite parameter models, the distribution theory of spectral estimates with applications to statistical inference, as well as sampling properties of spectral estimates, experimental design, and spectral computations. The book is intended either as a textbook or for individual reading for one-semester or two-quarter course for students of time series analysis users. It is also suitable for mathematicians or professors of calculus, statistics, and advanced mathematics.

The Spectral Analysis of Time Series

1995-05-18 Mathematics
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Release : 1995-05-18
Genre : Mathematics
Kind : eBook
Book Rating : 569/5 ( reviews)

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Book Synopsis The Spectral Analysis of Time Series by : Lambert H. Koopmans

Download or read book The Spectral Analysis of Time Series written by Lambert H. Koopmans. This book was released on 1995-05-18. Available in PDF, EPUB and Kindle. Book excerpt: To tailor time series models to a particular physical problem and to follow the working of various techniques for processing and analyzing data, one must understand the basic theory of spectral (frequency domain) analysis of time series. This classic book provides an introduction to the techniques and theories of spectral analysis of time series. In a discursive style, and with minimal dependence on mathematics, the book presents the geometric structure of spectral analysis. This approach makes possible useful, intuitive interpretations of important time series parameters and provides a unified framework for an otherwise scattered collection of seemingly isolated results.The books strength lies in its applicability to the needs of readers from many disciplines with varying backgrounds in mathematics. It provides a solid foundation in spectral analysis for fields that include statistics, signal process engineering, economics, geophysics, physics, and geology. Appendices provide details and proofs for those who are advanced in math. Theories are followed by examples and applications over a wide range of topics such as meteorology, seismology, and telecommunications.Topics covered include Hilbert spaces; univariate models for spectral analysis; multivariate spectral models; sampling, aliasing, and discrete-time models; real-time filtering; digital filters; linear filters; distribution theory; sampling properties ofspectral estimates; and linear prediction. - Hilbert spaces - univariate models for spectral analysis - multivariate spectral models - sampling, aliasing, and discrete-time models - real-time filtering - digital filters - linear filters - distribution theory - sampling properties of spectral estimates - linear prediction

Spectral Analysis for Univariate Time Series

2020-03-19 Mathematics
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Release : 2020-03-19
Genre : Mathematics
Kind : eBook
Book Rating : 175/5 ( reviews)

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Book Synopsis Spectral Analysis for Univariate Time Series by : Donald B. Percival

Download or read book Spectral Analysis for Univariate Time Series written by Donald B. Percival. This book was released on 2020-03-19. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Singular Spectrum Analysis for Time Series

2020-11-23 Mathematics
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Release : 2020-11-23
Genre : Mathematics
Kind : eBook
Book Rating : 362/5 ( reviews)

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Book Synopsis Singular Spectrum Analysis for Time Series by : Nina Golyandina

Download or read book Singular Spectrum Analysis for Time Series written by Nina Golyandina. This book was released on 2020-11-23. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an overview of singular spectrum analysis (SSA). SSA is a technique of time series analysis and forecasting combining elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. SSA is multi-purpose and naturally combines both model-free and parametric techniques, which makes it a very special and attractive methodology for solving a wide range of problems arising in diverse areas. Rapidly increasing number of novel applications of SSA is a consequence of the new fundamental research on SSA and the recent progress in computing and software engineering which made it possible to use SSA for very complicated tasks that were unthinkable twenty years ago. In this book, the methodology of SSA is concisely but at the same time comprehensively explained by two prominent statisticians with huge experience in SSA. The book offers a valuable resource for a very wide readership, including professional statisticians, specialists in signal and image processing, as well as specialists in numerous applied disciplines interested in using statistical methods for time series analysis, forecasting, signal and image processing. The second edition of the book contains many updates and some new material including a thorough discussion on the place of SSA among other methods and new sections on multivariate and multidimensional extensions of SSA.

The Spectral Analysis of Time Series

1974 Mathematics
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Release : 1974
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis The Spectral Analysis of Time Series by : Lambert Herman Koopmans

Download or read book The Spectral Analysis of Time Series written by Lambert Herman Koopmans. This book was released on 1974. Available in PDF, EPUB and Kindle. Book excerpt: The Spectral Analysis of Time Series ...

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