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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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($\infty$), 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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1488423804

Digital Object Identifier
doi:10.1214/17-EJS1241

Mathematical Reviews number (MathSciNet)
MR3619313

Zentralblatt MATH identifier
06702351

Subjects
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

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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