Time Series with Mixed Spectra

Author: Ta-Hsin Li
Publisher: CRC Press
ISBN: 1420010069
Format: PDF, ePub
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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.

A New Approach to Time Series with Mixed Spectra

Author: George Ronald Hext
Publisher:
ISBN:
Format: PDF, Docs
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The time series considered have jumps in their spectral distribution function; that is, the series is the sum of a 'signal' component, comprising a finite linear sum of pure sine-waves, and a 'noise' component, having continuous spectral density function. Given a set of observations from such a time series the primary problem is to estimate the 'signal' frequencies, the power in each component of the signal, and the 'noise' spectral density at these frequencies. The essence of the method used is as follows. For a given set of observations from such a series, and for each frequency that might yield a signal component, several estimates of the spectral density are made, using spectral windows of different bandwidths. To a first approximation, the noise component of the estimate is the same for every window, while the part of the estimate due to the signal is inversely proportional to the bandwidth of the window. Thus using a regression technique, one can separate the signal power from the noise spectral density at the given frequency and estimate these two quantities. These ideas are developed as follows. After a historical introduction, the early part of the thesis is devoted to the 'probability' aspects of the problem. First some results are proved that apply to the 'noise' series or any stationary time series. They give extensions and refinements of early approximations for the expected value of the spectral estimate, and for the covariance between two spectral estimates; these include the rates at which the limiting values are attained.

Nonstationarities in Hydrologic and Environmental Time Series

Author: A.R. Rao
Publisher: Springer Science & Business Media
ISBN: 9401001170
Format: PDF, ePub, Docs
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Conventionally, time series have been studied either in the time domain or the frequency domain. The representation of a signal in the time domain is localized in time, i.e . the value of the signal at each instant in time is well defined . However, the time representation of a signal is poorly localized in frequency , i.e. little information about the frequency content of the signal at a certain frequency can be known by looking at the signal in the time domain . On the other hand, the representation of a signal in the frequency domain is well localized in frequency, but is poorly localized in time, and as a consequence it is impossible to tell when certain events occurred in time. In studying stationary or conditionally stationary processes with mixed spectra , the separate use of time domain and frequency domain analyses is sufficient to reveal the structure of the process . Results discussed in the previous chapters suggest that the time series analyzed in this book are conditionally stationary processes with mixed spectra. Additionally, there is some indication of nonstationarity, especially in longer time series.

Time Series Analysis and Cyclostratigraphy

Author: Graham P. Weedon
Publisher: Cambridge University Press
ISBN: 9781139435178
Format: PDF, ePub, Mobi
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Increasingly environmental scientists, palaeoceanographers and geologists are collecting quantitative records of environmental changes (time-series) from sediments, ice cores, cave calcite, corals and trees. This book explains how to analyse these records, using straightforward explanations and diagrams rather than formal mathematical derivations. All the main cyclostratigraphic methods are covered including spectral analysis, cross-spectral analysis, filtering, complex demodulation, wavelet and singular spectrum analysis. Practical problems of time-series analysis, including those of distortions of environmental signals during stratigraphic encoding, are considered in detail. Recent research into various types of tidal and climatic cycles is summarised. The book ends with an extensive reference section, and an appendix listing sources of computer algorithms. This book provides the ideal reference for all those using time-series analysis to study the nature and history of climatic and tidal cycles. It is suitable for senior undergraduate and graduate courses in environmental science, palaeoceanography and geology.

The Spectral Analysis of Time Series

Author: L. H. Koopmans
Publisher: Academic Press
ISBN: 1483218546
Format: PDF
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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.

Univariate Time Series in Geosciences

Author: Hans Gilgen
Publisher: Springer Science & Business Media
ISBN: 3540309683
Format: PDF
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This is a detailed introduction to the statistical analysis of geophysical time series, using numerous examples and exercises to build proficiency. The exercises lead the reader to explore the meaning of concepts such as the estimation of the linear time series (AMRA) models or spectra. The book also serves as a guide to using the open-source "R" program for statistical analysis of time series.

Analysis of Economic Time Series

Author: Marc Nerlove
Publisher: Academic Press
ISBN: 1483218880
Format: PDF, ePub, Docs
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Analysis of Economic Time Series: A Synthesis integrates several topics in economic time-series analysis, including the formulation and estimation of distributed-lag models of dynamic economic behavior; the application of spectral analysis in the study of the behavior of economic time series; and unobserved-components models for economic time series and the closely related problem of seasonal adjustment. Comprised of 14 chapters, this volume begins with a historical background on the use of unobserved components in the analysis of economic time series, followed by an Introduction to the theory of stationary time series. Subsequent chapters focus on the spectral representation and its estimation; formulation of distributed-lag models; elements of the theory of prediction and extraction; and formulation of unobserved-components models and canonical forms. Seasonal adjustment techniques and multivariate mixed moving-average autoregressive time-series models are also considered. Finally, a time-series model of the U.S. cattle industry is presented. This monograph will be of value to mathematicians, economists, and those interested in economic theory, econometrics, and mathematical economics.