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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dean P. Foster & Daniel B. Nelson, 1994.
"Continuous Record Asymptotics for Rolling Sample Variance Estimators,"
NBER Technical Working Papers
0163, National Bureau of Economic Research, Inc.
- Foster, Dean P & Nelson, Daniel B, 1996. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," Econometrica, Econometric Society, vol. 64(1), pages 139-74, January.
- 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.
- Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
- Stanton, Richard, 1997. " A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- repec:cup:cbooks:9780521608275 is not listed on IDEAS
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- Westerfield, Janice Moulton, 1977. "An examination of foreign exchange risk under fixed and floating rate regimes," Journal of International Economics, Elsevier, vol. 7(2), pages 181-200, May.
- Wei Biao Wu & Zhibiao Zhao, 2007. "Inference of trends in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 391-410.
- repec:cup:cbooks:9780521845731 is not listed on IDEAS
- Yacine Aït-Sahalia & Jean Jacod, 2008. "Fisher's Information for Discretely Sampled Lévy Processes," Econometrica, Econometric Society, vol. 76(4), pages 727-761, 07.
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:153:y:2009:i:1:p:83-92. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.