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Journal of Time Series Analysis, 1983
Abstract. The ranks of certain matrices composed of autocovariances of an ARMA process are considered. These matrices arise in connection with initial estimates of the parameters of such a system. Conditions for such matrices to be of full rank are expressed in terms of conditions on a dual time reversed system.
An, Hong-Zhi +2 more
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Abstract. The ranks of certain matrices composed of autocovariances of an ARMA process are considered. These matrices arise in connection with initial estimates of the parameters of such a system. Conditions for such matrices to be of full rank are expressed in terms of conditions on a dual time reversed system.
An, Hong-Zhi +2 more
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The Identification of ARMA Models
Biometrika, 1990SUMMARY We present a new powerful method for determining the order of ARMA (p, q) models having small sets of observations. The procedure is based on an autoregressive order determination criterion and on linear estimation methods. Simulated data are used to demonstrate the capabilities of the approach. for a survey.
TARMO PUKKILA +2 more
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IEEE Transactions on Signal Processing, 1994
Parametric modeling of multichannel time series is accomplished by using higher (than second) order statistics (HOS) of the observed nonGaussian data. Cumulants of vector processes are defined using a Kronecker product formulation, and consistency of their sample estimators is addressed.
Ananthram Swami +2 more
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Parametric modeling of multichannel time series is accomplished by using higher (than second) order statistics (HOS) of the observed nonGaussian data. Cumulants of vector processes are defined using a Kronecker product formulation, and consistency of their sample estimators is addressed.
Ananthram Swami +2 more
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A NOTE ON ARMA PARAMETERISATION*
Australian Journal of Statistics, 1995SummaryThis paper considers the relationship between ARMA parameterisations of models fory(t)andAy(t), whereAis invertible andy(t)is a vector time series (t = 0,±1,…). An ARMA model for the transformed seriesAy(t)may have fewer parameters than a model fory(t).This paper shows that such a saving is illusory because the apparently saved parameters are ...
Hannan, E. J., Kavalieris, L.
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Spectral estimation of ARMA processes using ARMA-cepstrum recursion
IEEE Signal Processing Letters, 2000In this letter, the spectral estimation problem of a stationary autoregressive moving average (ARMA) process is considered, and a new method for the estimation of the MA part is proposed. A simple recursion relating the ARMA parameters and the cepstral coefficients of an ARMA process is derived and utilized for the estimation of the MA parameters.
Ali Kaderli, A. Salim Kayhan
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IEEE Transactions on Signal Processing, 2000
Summary: Autoregressive-moving-average (ARMA) models seek to express a system function of a discretely sampled process as a rational function in the \(z\)-domain. Treating an ARMA model as a complex rational function, we discuss a metric defined on the set of complex rational functions.
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Summary: Autoregressive-moving-average (ARMA) models seek to express a system function of a discretely sampled process as a rational function in the \(z\)-domain. Treating an ARMA model as a complex rational function, we discuss a metric defined on the set of complex rational functions.
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1986
This paper deals with the ubiquitous class of linear time-invariant finite dimensional systems. In [1] it has been shown that this is precisely the class of AR systems, that is, the dynamical systems whose behavior is governed by a finite set of autoregressive relations.
NIEUWENHUIS, JW, WILLEMS, JC
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This paper deals with the ubiquitous class of linear time-invariant finite dimensional systems. In [1] it has been shown that this is precisely the class of AR systems, that is, the dynamical systems whose behavior is governed by a finite set of autoregressive relations.
NIEUWENHUIS, JW, WILLEMS, JC
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The Misspecification of Arma Models
Statistica Neerlandica, 1989The object of this paper is to assess the effects of fitting a model of the wrong order to a time series which is generated by an autoregressive moving–average process. The method is to examine the spectral density functions which are indicated by the probability limits of the least–squares estimators of the misspecified models.
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ARMA-models and their equivalences
International Journal of Control, 2009The classical theory of ‘strict system equivalence’ of Rosenbrock and Fuhrmann is presented in a very general setting, namely, in the setting of ARMA-models defined over an arbitrary commutative ring.
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