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: 9780521019835
Format: PDF, ePub, Mobi
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An essential reference for researchers, and 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, Docs
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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, Docs
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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.

Climate Time Series Analysis

Author: Manfred Mudelsee
Publisher: Springer Science & Business Media
ISBN: 9789048194827
Format: PDF, Docs
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Climate is a paradigm of a complex system. Analysing climate data is an exciting challenge, which is increased by non-normal distributional shape, serial dependence, uneven spacing and timescale uncertainties. This book presents bootstrap resampling as a computing-intensive method able to meet the challenge. It shows the bootstrap to perform reliably in the most important statistical estimation techniques: regression, spectral analysis, extreme values and correlation. This book is written for climatologists and applied statisticians. It explains step by step the bootstrap algorithms (including novel adaptions) and methods for confidence interval construction. It tests the accuracy of the algorithms by means of Monte Carlo experiments. It analyses a large array of climate time series, giving a detailed account on the data and the associated climatological questions. This makes the book self-contained for graduate students and researchers.

Time Series Analysis and Its Applications

Author: Robert H. Shumway
Publisher: Springer
ISBN: 3319524526
Format: PDF, ePub, Mobi
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The fourth edition of this popular graduate textbook, like its predecessors, presents a balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. Numerous examples using nontrivial data illustrate solutions to problems such as discovering natural and anthropogenic climate change, evaluating pain perception experiments using functional magnetic resonance imaging, and monitoring a nuclear test ban treaty. The book is designed as a textbook for graduate level students in the physical, biological, and social sciences and as a graduate level text in statistics. Some parts may also serve as an undergraduate introductory course. Theory and methodology are separated to allow presentations on different levels. In addition to coverage of classical methods of time series regression, ARIMA models, spectral analysis and state-space models, the text includes modern developments including categorical time series analysis, multivariate spectral methods, long memory series, nonlinear models, resampling techniques, GARCH models, ARMAX models, stochastic volatility, wavelets, and Markov chain Monte Carlo integration methods. This edition includes R code for each numerical example in addition to Appendix R, which provides a reference for the data sets and R scripts used in the text in addition to a tutorial on basic R commands and R time series. An additional file is available on the book’s website for download, making all the data sets and scripts easy to load into R.