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

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Post-edited
Authors : Bardet, Jean-Marc (Author of the conference)
CIRM (Publisher )

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causal affine models GARCH models stationarity Gaussian quasi-maximum likelihood estimator first limit theorems Laplacian quasi-maximum likelihood estimator second limit theorems Laplacian QMLE simulation results Gaussian vs Laplacian QMLE questions of the audience
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.

MSC Codes :
62F12 - Asymptotic properties of estimators
 62M10 - Time series, auto-correlation, regression, etc.
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 02/03/16
    Conference Date : 16/02/16
    Subseries : Research talks
    arXiv category : Statistics Theory
    Mathematical Area(s) : Probability & Statistics
    Format : MP4 (.mp4) - HD
    Video Time : 00:36:51
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2016-02-16_Bardet.mp4
Information on the Event

Event Title : Thematic month on statistics - Week 3: Processus / Mois thématique sur les statistiques - Semaine 3 : Processus
Event Organizers : Boutahar, Mohamed ; Reboul, Laurence
Dates : 15/02/16 - 19/02/16
Event Year : 2016
Event URL : http://conferences.cirm-math.fr/1617.html

Citation Data

DOI : 10.24350/CIRM.V.18931403
Cite this video as: Bardet, Jean-Marc (2016). Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18931403
URI : http://dx.doi.org/10.24350/CIRM.V.18931403

See Also

Bibliography

  • [1] Bardet, J.-M., Boularouk, Y., Djaballah, K. (2016). Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes. - 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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