4115 articles – 7312 references  [version française]
 HAL: hal-00442875, version 1
 arXiv: 0912.4686
 Robust estimation of the scale and of the autocovariance function of Gaussian short and long-range dependent processes
 (2009-12-23)
 A desirable property of an autocovariance estimator is to be robust to the presence of additive outliers. It is well-known that the sample autocovariance, being based on moments, does not have this property. Hence, the use of an autocovariance estimator which is robust to additive outliers can be very useful for time-series modeling. In this paper, the asymptotic properties of the robust scale and autocovariance estimators proposed by Rousseeuw and Croux (1993) and Genton and Ma (2000) are established for Gaussian processes, with either short-range or long-range dependence. It is shown in the short-range dependence setting that this robust estimator is asymptotically normal at the rate $\sqrt{n}$, where $n$ is the number of observations. An explicit expression of the asymptotic variance is also given and compared to the asymptotic variance of the classical autocovariance estimator. In the long-range dependence setting, the limiting distribution displays the same behavior than that of the classical autocovariance estimator, with a Gaussian limit and rate $\sqrt{n}$ when the Hurst parameter $H$ is less $3/4$ and with a non-Gaussian limit (belonging to the second Wiener chaos) with rate depending on the Hurst parameter when $H \in (3/4,1)$. Some Monte-Carlo experiments are presented to illustrate our claims and the Nile River data is analyzed as an application. The theoretical results and the empirical evidence strongly suggest using the robust estimators as an alternative to estimate the dependence structure of Gaussian processes.
 1: Laboratoire Traitement et Communication de l'Information [Paris] (LTCI) Télécom ParisTech – CNRS : UMR5141 2: Groupe de recherche en économie mathématique et quantitative (GREMAQ) CNRS : UMR5604 – Université des Sciences Sociales - Toulouse I – École des Hautes Études en Sciences Sociales [EHESS] – Institut national de la recherche agronomique (INRA) : UMR 3: Department of Mathematics - Boston University Boston University 4: Universade Federal Do Espirito Santo Universade Federal Do Espirito Santo
 Subject : Mathematics/StatisticsStatistics/Statistics Theory
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 hal-00442875, version 1 http://hal.archives-ouvertes.fr/hal-00442875 oai:hal.archives-ouvertes.fr:hal-00442875 From: Céline Lévy-Leduc <> Submitted on: Wednesday, 23 December 2009 12:00:36 Updated on: Wednesday, 23 December 2009 17:52:12