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Asymptotic theory for M estimators for martingale differences with applications to GARCH models

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  • Tinkl, Fabian
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    Abstract

    We generalize the results for statistical functionals given by [Fernholz, 1983] and [Serfling, 1980] to M estimates for samples drawn for an ergodic and stationary martingale sequence. In a first step, we take advantage of some recent results on the uniform convergency of the empirical distribution given by [Adams & Nobel, 2010] to prove consistency of M estimators, before we assume Hadamard differentiability of our estimators to prove their asymptotic normality. Further we apply the results to the LAD estimator of [Peng & Yao, 2003] and the maximum-likelihood estimator for GARCH processes to show the wide field of possible applications of this method. --

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    Bibliographic Info

    Paper provided by Friedrich-Alexander-Universität Erlangen-Nürnberg, Institut für Wirtschaftspolitik und Quantitative Wirtschaftsforschung (IWQW) in its series IWQW Discussion Paper Series with number 09/2010.

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    Date of creation: 2010
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    Handle: RePEc:zbw:iwqwdp:092010

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    Web page: http://www.iwqw.rw.uni-erlangen.de/
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    Keywords: Hadamard differential; M estimator; von Mises Calculus; martingale differences; GARCH models;

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    1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
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