## Electronic Journal of Statistics

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

#### 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
First available in Project Euclid: 2 March 2017

https://projecteuclid.org/euclid.ejs/1488423804

Digital Object Identifier
doi:10.1214/17-EJS1241

Mathematical Reviews number (MathSciNet)
MR3619313

Zentralblatt MATH identifier
06702351

#### 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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