Asymptotic theory for M estimators for martingale differences with applications to GARCH models
AbstractWe 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 InfoPaper 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.
Date of creation: 2010
Date of revision:
Hadamard differential; M estimator; von Mises Calculus; martingale differences; GARCH models;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-11-20 (All new papers)
- NEP-ECM-2010-11-20 (Econometrics)
- NEP-ETS-2010-11-20 (Econometric Time Series)
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- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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