Electronic Journal of Statistics

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

Jean-Marc Bardet, Yakoub Boularouk, and Khedidja Djaballah

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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($\infty$), GARCH, ARCH($\infty$), 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.

Article information

Electron. J. Statist., Volume 11, Number 1 (2017), 452-479.

Received: April 2016
First available in Project Euclid: 2 March 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60G10: Stationary processes

Laplacian quasi-maximum likelihood estimator strong consistency asymptotic normality ARMA-ARCH processes

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Bardet, Jean-Marc; Boularouk, Yakoub; Djaballah, Khedidja. Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes. Electron. J. Statist. 11 (2017), no. 1, 452--479. doi:10.1214/17-EJS1241. https://projecteuclid.org/euclid.ejs/1488423804

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