Filling this void, Time Series with Mixed Spectra focuses on the methods and theory for the stati
Author: Ta-Hsin Li
Publisher: CRC Press
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.
For two or more time series with spectral density functions of the same structure ,
this result does not in general hold . 1 . 3 . Examples of Time Series with Mixed Spectra . Before exploring their properties further , we shall first see how time ...
Author: George Ronald Hext
Category: Time-series analysis
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.
... 17 p3370 N66-30259 Time series with mixed spectra signal power and noise
spectral density studies ( AROD - 2025-16 ) 17 p3371 N66-30664 Methods for
exact linear prediction of stationary time series by least squares method 20
( 11 ] Priestley , M. B. ( 1981 ) , Spectral Analysis and Time Series , Vols . ...
analysis of Seiche record , J. Marine Research , 13 , 76100 . a of 19 ] Priestley ,
M. B. ( 1962a ) , The analysis stationary processes with mixed spectra - I , J.R.
In fact , this serves as a useful theoretical criterion for distinguishing between time series with continuous and discrete or mixed spectra . However , it is possible
that | C ( 7 ) | goes to zero so slowly that the usual inversion methods fail . This is
Author: United States. Bureau of the CensusPublish On: 1954
The Spectral Analysis of Economic Time Series , " Bureau of the Census Working
Paper No. ... Estimation of Parameters in Time Series Regression Models , " J.
Roy . Stat . ... The Analysis of Stationary Processes with Mixed Spectra I " , J. Roy
9.7.1 Two - dimensional Mixed Spectra In Chapter 8 we referred briefly to the
multidimensional version of the mixed spectra problem , and pointed out that the
types of discontinuities which could arise were more complicated than in the one
... periodogram of a time series. An asymptotic analysis reveals a connection
between the Laplace periodogram and the zero-crossing spectrum. ... We also
discuss its usefulness for time series of mixed spectra. Finally, we provide a real-
Koopmans L.H., 1974, The Spectral Analysis of Time Series (Academic Press,
London). Koževnikova I.A. ... Priestley M.B., 1962, The analysis of stationary
processes with mixed spectra, J. Royal Statistical Society B24 511–529. Rabiner
Author: I. G. Žurbenko
Publisher: North Holland
Examined in this volume are the asymptotic properties of spectral estimates of stationary processes and random fields. A new class of lag window estimates indifferent to remote frequencies is introduced and pseudorandom sequences are investigated from the point of view of their nearness to the sequence of white noise. Principles and algorithms are given for constructing an ideal sequence. A good achievement is the new estimates of higher spectral density asymptotically unbiased and consistent for all admissible values of the argument. A new type of the random number generator which is sufficiently close to white noise is introduced.
spectra, we must distinguish two general cases: the observed time series are
jointly covariance stationary with absolutely continuous spectrum and have: (1)
zero means, (2) possibly nonzero means. We call the second case the mixed ...
A new approach to time series with mixed spectra . ” Unpublished Ph . D .
dissertation , Stanford Univ . Hicks , J . R . ( 1939 ) . Value and Capital , 1st ed .
London and New York : Oxford Univ . Press . Holt , C . C . , Modigliani , F . , Muth ,
J . F .
Author: Marc Nerlove
In this edition which has been reprinted with corrections, Nerlove and his co-authors illustrate techniques of spectral analysis and methods based on parametric models in the analysis of economic time series. The book provides a means and a method for incorporating economic intuition and theory in the formulation of time-series models useful in forecasting, in the formulation and estimation of distributed lag models, and in other applications, such as seasonal adjustment. Analysis of Economic Time Series is a useful primary text for graduate students and an attractive reference for researchers. Key Features * Presents a self-contained treatment of Fourier Analysis and complex variables, as well as Spectral Analysis of time series * Includes a detailed treatment of unobserved-components (UC) models and their time-series properties by means of covariance-generating transforms * Provides the formulation and maximum-likelihood estimation of ARMA and UC models in both time and frequency domains Integrates several topics in time-series analysis: * The formulation and estimation of distributed-lag models of dynamic economic behavior * The application of the techniques of spectral analysis in the study of behavior of economic time series * Unobserved-components models for economic time series and the closely related problem of seasonal adjustment * The complimentarities between time-domain and frequency-domain approaches to the analysis of economic time series * Historical contributions extending from the time of Charles Babbage and the Edinburgh Review to the present * Treats spectral analysis and Box-Jenkins models for an intuitive but rigorous point of view * Shows how these two types of analysis may be synthesized so that they complement one another * Describes a new type of model, based on a superposition of Box-Jenkins models, that captures the essential idea of the unobserved-components models long used in the analysis of economic time series * Applies multiple time-series techniques to the estimation of a novel dynamic model of the US cattle industry
determination of periodicities from the periodogram has implicitly implied that any
spectral lines occur at Fourier frequencies , this may be problematic for small
sample ... Semiparametric Bayesian inference for time series with mixed spectra .
Author: Indian Statistical AssociationPublish On: 1967
FOR DISCRIMINATION BETWEEN DISCRETE , CONTINUOUS AND MIXED SPECTRA OF A STATIONARY TIME SERIES J. Medhi and T. Subba Rao1
Gauhati University SUMMARY The applicability of the sequential and non -
sequential test ...
CROSS SPECTRAL DISTRIBUTION THEORY FOR MIXED SPECTRA AND
ESTIMATION OF PREDICTION FILTER ... Secondly , an approximate distribution
theory of the sample coefficient of coherence , when the time series have
Author: Board of Governors of the Federal Reserve System (U.S.)Publish On: 1972
Box , G . E . P . , and Jenkins , G . M . Time Series Analysis , Forecasting and
Control . ... The Typical Spectral Shape of an Economic Variable , ” Econometrica
, Vol . ... Hext , George R . " A New Approach to Time Series with Mixed Spectra .
Author: Board of Governors of the Federal Reserve System (U.S.)
Minimum distance approach in parametric estimation 103-18 Mixed spectra
grouped periodogram test 85-6 Hannan's test 83-4 P ( 2 ) test 81-3 relationship
between Hannan's estimate and P ( 2 ) 84-5 Whittle's test 79–81 Modelling of
Author: T. Subba Rao
Publisher: Chapman and Hall/CRC
Very Good,No Highlights or Markup,all pages are intact.
INFERENCE FOR TIME SERIES WITH MIXED SPECTRUM Shean - Tsong CHIU
, Rice University , Houston . The old and important problem of estimating the
discontinuous ( mixed ) spectrum of a series containing periodic components is ...
There are , however , times when it is important to distinguish between this
concept of a mixed spectrum and the ... The detection of discrete mass , or a
close approximation thereof , in the cross - spectrum of two time series is a signal
to search ...
Author: R. P. Gupta
Publisher: Amsterdam : North-Holland
Category: Analyse multivariée - Congrès
Tests of multiple correlation with additional data; On D-, E-, DA- and DM - optimality properties of test procedures of hypotheses concerning the covariance matrix of a normal distribution; Scaling of multi-dimensional contingency tables by union-intersection; The negative binomial point process and its inference; Tests of location based on principal components; Invariant polynomials with matrix arguments and their applications; A nonparametric method to discriminate two populations; Some methods of searching for outliers; On a multivariate statistical classification model; Some applications of conditional expectation minimization theory to psychological tests; An application of the singular normal distribution in linear models; Asymptotic distribution ofquantiles from a multivariate distribution; Distributional properties of certain tests for detection of discrete mass in cross-spectra of multivariate time series; The effects of elliptical distribution on some standard procedures involving correlation coefficients: a review ...
It seeks to compare : ( 1 ) Spectral approaches to finding relations among time series , ( 2 ) Time domain or innovation ... of efficient estimation of the parameters
of moving average and mixed scheme models for time series ; ( 2 ) to compare ...