Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes

Jean Marc Bardet; Yakoub Boularouk; Khedidja Djaballah

doi:10.1214/17-EJS1241

Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes

Jean Marc Bardet
, Yakoub Boularouk
, Khedidja Djaballah

Université Panthéon-Sorbonne (Paris 1)
Université des Sciences et de la Technologie Houari Boumediène

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We prove the consistency and asymptotic normality of the Laplacian Quasi-Maximum Likelihood Estimator (QMLE) for a general class of causal time series including ARMA, AR(∞), GARCH, ARCH(∞), ARMA-GARCH, APARCH, ARMA-APARCH,.., processes. We notably exhibit the advantages (moment order and robustness) of this estimator compared to the classical Gaussian QMLE. Numerical simulations confirms the accuracy of this estimator.

langue originale	Anglais
Pages (de - à)	452-479
Nombre de pages	28
journal	Electronic Journal of Statistics
Volume	11
Numéro de publication	1
Les DOIs	https://doi.org/10.1214/17-EJS1241
état	Publié - 1 janv. 2017
Modification externe	Oui

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10.1214/17-EJS1241

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abstract = "We prove the consistency and asymptotic normality of the Laplacian Quasi-Maximum Likelihood Estimator (QMLE) for a general class of causal time series including ARMA, AR(∞), GARCH, ARCH(∞), ARMA-GARCH, APARCH, ARMA-APARCH,.., processes. We notably exhibit the advantages (moment order and robustness) of this estimator compared to the classical Gaussian QMLE. Numerical simulations confirms the accuracy of this estimator.",

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N2 - We prove the consistency and asymptotic normality of the Laplacian Quasi-Maximum Likelihood Estimator (QMLE) for a general class of causal time series including ARMA, AR(∞), GARCH, ARCH(∞), ARMA-GARCH, APARCH, ARMA-APARCH,.., processes. We notably exhibit the advantages (moment order and robustness) of this estimator compared to the classical Gaussian QMLE. Numerical simulations confirms the accuracy of this estimator.

AB - We prove the consistency and asymptotic normality of the Laplacian Quasi-Maximum Likelihood Estimator (QMLE) for a general class of causal time series including ARMA, AR(∞), GARCH, ARCH(∞), ARMA-GARCH, APARCH, ARMA-APARCH,.., processes. We notably exhibit the advantages (moment order and robustness) of this estimator compared to the classical Gaussian QMLE. Numerical simulations confirms the accuracy of this estimator.

KW - ARMA-ARCH processes

KW - Asymptotic normality

KW - Laplacian quasi-maximum likelihood estimator

KW - Strong consistency

UR - https://www.scopus.com/pages/publications/85014754641

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Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes

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