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

Fabian Tinkl

No 09/2010, FAU Discussion Papers in Economics from Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics

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.

Keywords: Hadamard differential; M estimator; von Mises Calculus; martingale differences; GARCH models (search for similar items in EconPapers)
Date: 2010
New Economics Papers: this item is included in nep-ecm and nep-ets
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:iwqwdp:092010

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