Nonparametric inference of discretely sampled stable Lévy processes
AbstractWe study nonparametric inference of stochastic models driven by stable Lévy processes. We introduce a nonparametric estimator of the stable index that achieves the parametric rate of convergence. For the volatility function, due to the heavy-tailedness, the classical least-squares method is not applicable. We then propose a nonparametric least-absolute-deviation or median-quantile estimator and study its asymptotic behavior, including asymptotic normality and maximal deviations, by establishing a representation of Bahadur-Kiefer type. The result is applied to several major foreign exchange rates.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 153 (2009)
Issue (Month): 1 (November)
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Web page: http://www.elsevier.com/locate/jeconom
Bahadur-Kiefer representation Levy process Nonparametric estimation Quantile regression Spot volatility Stable index Stable process;
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