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

De Jean-Marc Bardet

Apparaît dans la collection : Thematic month on statistics - Week 3: Processus / Mois thématique sur les statistiques - Semaine 3 : Processus

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.

Informations sur la vidéo

Date de captation 16/02/2016
Date de publication 02/03/2016
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.18931403
Citer cette vidéo Bardet, Jean-Marc (16/02/2016). Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18931403
URL https://dx.doi.org/10.24350/CIRM.V.18931403

Domaine(s)

Statistiques - Théorie

Bibliographie

[1] Bardet, J.-M., Boularouk, Y., Djaballah, K. (2016). Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes. <arXiv:1601.00155> - http://arxiv.org/abs/1601.00155
[2] Bardet, J.-M., & Wintenberger, O. (2009). Asymptotic normality of the Quasi-Maximum likelihood estimator for multidimensional causal process. The Annals of Statistics, 37(5B), 2730-2759 - http://dx.doi.org/10.1214/08-AOS674
[3] Berkes, I., Horváth, L., & Kokoszka, P. (2003). GARCH processes: structure and estimation. Bernoulli, 9(2), 201-227 - http://dx.doi.org/10.3150/bj/1068128975
[4] Ding, Z., Granger C.W.J. and Engle R.F. (1993). A Long Memory Property of Stock Market Returns and a New Model. Journal of Empirical Finance, 1(1), 83-106 - http://dx.doi.org/10.1016/0927-5398(93)90006-D
[5] Francq, C. and Zakoian, J-M. (2013) Optimal predictions of powers of conditionally heteroskedastic processes. Journal of the Royal Statistical Society B, 75(2), 345-367 - http://dx.doi.org/10.1111/j.1467-9868.2012.01045.x

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