Multiple Time Series

Hannan, E. J.; Raghavarao, Damaraju; Lancaster, H. O.

doi:10.2307/3151167

Cited by 121 publications

(171 citation statements)

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“…Therefore, as noted by Battaglia [13] , unless the matrix polynomials, L(z) and H(z), commute, L(z)H(z)=H(z)L(z), the inverse process, Yi(t), may not be expressed in the form of a standard VARMA model defined by equation (11). Although the class of VARMA models with commuting AR and MA polynomials is not sparse and it, for example, includes the univariate ARMA as well as the pure VAR and pure VMA models as members, this particular requirement does seem to severely limit the possible applications of the inverse correlations for specifying a VARMA model.…”

Section: Properties Of the Inverse Processmentioning

confidence: 99%

“…satisfy Assumption 1 and suppose that X(t) is unknown for a fixed t. The question of how to construct an optimal linear estimate of X(t) from a knowledge of {X(t-j),j≠0} is known as the problem of linear interpolation [11] . Examples of situations where a question of this type arises include the problem of outlier detection and estimation of missing values for a multivariate time series, analysis of spatial data collected over a narrow but long rectangular lattice [12] and spatio-temporal processes.…”

Section: Inverse Process and The Linear Interpolatormentioning

confidence: 99%

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Inverse Correlations for Multiple Time Series and Gaussian Random Fields and Measures of Their Linear Determinism

Majdi¹

2005

Journal of Mathematics and Statistics

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For a discrete-time vector linear stationary process, {X(t)}, admitting forward and backward autoregressive representations, the variance matrix of an optimal linear interpolator of X(t), based on a knowledge of {X(t-j), j≠0}, is known to be given by Ri (0) The relationship between the matrix A and the corresponding matrix, P, obtained by considering only an optimal one-step linear predictor of X(t) from a knowledge of its infinite past, {X(t-j),j>0}, is also discussed. The possible role the inverse correlation function may have for model specification of a vector ARMA model is explored. Close parallels between the problem of interpolation for a stationary univariate two-dimensional Gaussian random field and time series are examined and an index of linear determinism for the latter class of processes is also defined. An application of this index for model specification and diagnostic testing of a Gaussian Markov Random Field is investigated together with the question of its estimation from observed data. Results are illustrated by a simulation study.

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Section: Properties Of the Inverse Processmentioning

confidence: 99%

Section: Inverse Process and The Linear Interpolatormentioning

confidence: 99%

Inverse Correlations for Multiple Time Series and Gaussian Random Fields and Measures of Their Linear Determinism

Majdi¹

2005

Journal of Mathematics and Statistics

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“…Our requirement (2.10) for X M t is stronger.) Grenander shows that the real matrix sequence U k , k = 0; 1; : : : has a representation U k = R e ik dG U ( ) in which G U ( ) is an Hermitian-matrix-valued function such that the eigenvalues of increments G U ( 2 ) G U ( 1 ), 2 1 , are non-negative, or, equivalently, the increments are Hermitian nonnegative; see also Grenander and Rosenblatt (1984), Chapter II of Hannan (1970), and Chapter 10 of Anderson (1971). For example, if …”

Section: B Scalable Asymptotic Stationaritymentioning

confidence: 99%

Optimality of GLS for One-Step-Ahead Forecasting With Regarima and Related Models When the Regression Is Misspecified

Findley

2007

Econ. Theory

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We consider the modeling of a time series described by a linear regression component whose regressor sequence satis…es the generalized asymptotic sample second moment stationarity conditions of Grenander (1954). The associated disturbance process is only assumed to have sample second moments that converge with increasing series length, perhaps after a di¤erencing operation. The model's regression component is taken to be underspeci…ed, due perhaps to simpli…cations, approximations, or parsimony. Also, the ARMA or ARIMA model used for the disturbances need not be correct. Both Ordinary Least Squares and Generalized Least Squares estimates of the mean function are considered. An optimality property of GLS relative to OLS is obtained for one-step-ahead forecasting. Asymptotic bias characteristics of the regression estimates are shown to distinguish the forecasting performance. The results provide theoretical support for a procedure used by Statistics Netherlands to impute the values of late reporters in some economic surveys.

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“…An important application of the WGN condition is as the null hypothesis in testing for colored noise. Tests for colored noise based on the periodogram [1] and serial autocorrelation function [2]- [4] have been studied.…”

Section: A Motivation and Previous Workmentioning

confidence: 99%

Multidimensional probability density function approximations for detection, classification, and model order selection

Kay

Nuttall

Baggenstoss

2001

IEEE Trans. Signal Process.

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Abstract-This paper addresses the problem of calculating the multidimensional probability density functions (PDFs) of statistics derived from known many-to-one transformations of independent random variables (RVs) with known distributions. The statistics covered in the paper include reflection coefficients, autocorrelation estimates, cepstral coefficients, and general linear functions of independent RVs. Through PDF transformation, these results can be used for general PDF approximation, detection, classification, and model order selection. A model order selection example that shows significantly better performance than the Akaike and MDL method is included.

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Multiple Time Series

Cited by 121 publications

References 0 publications

Inverse Correlations for Multiple Time Series and Gaussian Random Fields and Measures of Their Linear Determinism

Inverse Correlations for Multiple Time Series and Gaussian Random Fields and Measures of Their Linear Determinism

Optimality of GLS for One-Step-Ahead Forecasting With Regarima and Related Models When the Regression Is Misspecified

Multidimensional probability density function approximations for detection, classification, and model order selection

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