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

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  • Tinkl, Fabian

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.

Suggested Citation

  • Tinkl, Fabian, 2010. "Asymptotic theory for M estimators for martingale differences with applications to GARCH models," FAU Discussion Papers in Economics 09/2010, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
  • Handle: RePEc:zbw:iwqwdp:092010
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    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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    Keywords

    Hadamard differential; M estimator; von Mises Calculus; martingale differences; GARCH models;

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