Nonparametric inference of discretely sampled stable Lévy processes
We 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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- Yacine Aït-Sahalia & Jean Jacod, 2008. "Fisher's Information for Discretely Sampled Lévy Processes," Econometrica, Econometric Society, vol. 76(4), pages 727-761, 07.
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"A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data,"
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- Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2003. "A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data," NBER Working Papers 10111, National Bureau of Economic Research, Inc.
- repec:cup:cbooks:9780521845731 is not listed on IDEAS
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