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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	452-479
Number of pages	28
Journal	Electronic Journal of Statistics
Volume	11
Issue number	1
DOIs	https://doi.org/10.1214/17-EJS1241
Publication status	Published - 1 Jan 2017
Externally published	Yes

Keywords

ARMA-ARCH processes
Asymptotic normality
Laplacian quasi-maximum likelihood estimator
Strong consistency

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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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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

U2 - 10.1214/17-EJS1241

DO - 10.1214/17-EJS1241

M3 - Article

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SP - 452

EP - 479

JO - Electronic Journal of Statistics

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

Abstract

Keywords

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