Identification of non-minimum phase transfer function using higher-order spectrum

Kumon, Masayuki

doi:10.1007/bf00058639

Cited by 4 publications

(3 citation statements)

References 25 publications

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“…The extension to the conditional heteroskedasticity case is more challenging since this will affect the parametric form of f 4 and left open for future research. Kumon (1992) provides a CLT for Z-estimators based on higher order cumulants, which are asymptotically equivalent to the corresponding MD estimators. Notice that Kumon's formula (3.9), which provides the asymptotic variance of θ (3) T differs from ours due to two important aspects: he is not centering by μ(θ 0 ) in expression ( 16), which is needed for noninvertible processes, and the scaling in his expression (3.9) is adjusted by the fact that we only use the real part of the biperiodogram in the FOC.…”

Section: Asymptotic Properties Of Estimators Based On Minimizing a Weighted Linear Combination Of L *mentioning

confidence: 99%

“…Andrews, Davis and Breidt (2007) extend the previous article to rankestimators so they can dispose of the Laplacian assumption. Using also a two-step approach, Kumon (1992) proposes estimates based on the extension to higher order spectral densities of the frequency domain first order conditions of the Whittle (1953) estimate. Anh, Leonenko and Sakhno (2007) follow Kumon's approach, and propose estimates based on related estimating equations using weighted higher order periodograms.…”

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Frequency domain minimum distance inference for possibly noninvertible and noncausal ARMA models

Velasco¹,

Lobato²

2018

Ann. Statist.

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This article introduces frequency domain minimum distance procedures for performing inference in general, possibly non causal and/or noninvertible, autoregressive moving average (ARMA) models. We use information from higher order moments to achieve identification on the location of the roots of the AR and MA polynomials for non-Gaussian time series. We propose a minimum distance estimator that optimally combines the information contained in second, third, and fourth moments. Contrary to existing estimators, the proposed one is consistent under general assumptions, and may improve on the efficiency of estimators based on only second order moments. Our procedures are also applicable for processes for which either the third or the fourth order spectral density is the zero function.

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Section: Asymptotic Properties Of Estimators Based On Minimizing a Weighted Linear Combination Of L *mentioning

confidence: 99%

mentioning

confidence: 99%

Frequency domain minimum distance inference for possibly noninvertible and noncausal ARMA models

Velasco¹,

Lobato²

2018

Ann. Statist.

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“…Typically, non-Gaussianity is exploited for identification of dynamic models through conditions on higher order cumulants (Gouriéroux et al, 2019;Lanne and Luoto, 2019) or spectral densities (Lii and Rosenblatt, 1982;Kumon, 1992), but it has also been imposed through particular probability distribution assumptions on the shocks or with conditional (Normandin and Phaneuf, 2004) and unconditional heteroskedasticity conditions (Rigobon, 2003;Lanne and Lütkepohl, 2008), possibly with Markov switching dynamics (Lanne, Lütkepohl and Maciejowska, 2010;Lütkepohl and Netŝunajev, 2017). Then, estimation is performed using ML or approximate versions of it (e.g.…”

Section: Introductionmentioning

confidence: 99%

Identification and estimation of Structural VARMA models using higher order dynamics

Velasco¹

2020

Preprint

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We use information from higher order moments to achieve identification of non-Gaussian structural vector autoregressive moving average (SVARMA) models, possibly non-fundamental or non-causal, through a frequency domain criterion based on a new representation of the higher order spectral density arrays of vector linear processes. This allows to identify the location of the roots of the determinantal lag matrix polynomials based on higher order cumulants dynamics and to identify the rotation of the model errors leading to the structural shocks up to sign and permutation. We describe sufficient conditions for global and local parameter identification that rely on simple rank assumptions on the linear dynamics and on finite order serial and component independence conditions for the structural innovations. We generalize previous univariate analysis to develop asymptotically normal and efficient estimates exploiting second and non-Gaussian higher order dynamics given a particular structural shocks ordering without assumptions on causality or invertibility. Bootstrap approximations to finite sample distributions and the properties of numerical methods are explored with real and simulated data.

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Identification of transfer function matrix using higher-order spectra

Kumon

1996

Japan J. Indust. Appl. Math.

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This paper treats of the identification of parametric transfer function matrix. The method is based on the inner-outer factorization of a stable transfer function matrix. The outer part is identified by the use of the second-order spectral est• from the observed linear process, while the inner part is identified by the use of a higher-order cumulant spectral est• from the observed process. Respective parameter estimators are determined in the light of asymptotic efficiency. In order to est• the order of the inner part, a criterion IIC is introduced based on the same principle as in the case of Akaike's AIC.

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Identification of non-minimum phase transfer function using higher-order spectrum

Abstract: All-pass, asymptotic efficiency, cumulant spectrum, inner function, linear process, minimum phase, non-Gaussian, outer function,

Cited by 4 publications

References 25 publications

Frequency domain minimum distance inference for possibly noninvertible and noncausal ARMA models

Frequency domain minimum distance inference for possibly noninvertible and noncausal ARMA models

Identification and estimation of Structural VARMA models using higher order dynamics

Identification of transfer function matrix using higher-order spectra

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