Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 11, Number 1 (2017), 452-479.
Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes
Jean-Marc Bardet, Yakoub Boularouk, and Khedidja Djaballah
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