Exact inference and optimal invariant estimation for the stability parameter of symmetric [alpha]-stable distributions
Hill estimation (Hill, 1975), the most widespread method for estimating tail thickness of heavy-tailed financial data, suffers from two drawbacks. One is that the optimal number of tail observations to use in the estimation is a function of the unknown tail index being estimated, which diminishes the empirical relevance of the Hill estimation. The other is that the hypothesis test of the underlying data lying in the domain of attraction of an [alpha]-stable law ([alpha]Â =Â 2) for finite samples, is performed on the basis of the asymptotic distribution, which can be different from those for finite samples. In this paper, using the Monte Carlo technique, we propose an exact test method for the stability parameter of [alpha]-stable distributions which is based on the Hill estimator, yet is able to provide exact confidence intervals for finite samples. Our exact test method automatically includes an estimation procedure which does not need the assumption of a known number of observations on the distributional tail. Empirical applications demonstrate the advantages of our new method in comparison with the Hill estimation.
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.:
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- Andrews, Donald W K, 1993.
"Tests for Parameter Instability and Structural Change with Unknown Change Point,"
Econometric Society, vol. 61(4), pages 821-56, July.
- Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
- Johan Segers, 2002. "Abelian and Tauberian Theorems on the Bias of the Hill Estimator," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 461-483.
- Kim Jeong-Ryeol & Mittnik Stefan & Rachev Svetlozar T., 1996. "Detecting Asymmetries in Observed Linear Time Series and Unobserved Disturbances," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(3), pages 1-15, October.
- Huisman, Ronald, et al, 2001. "Tail-Index Estimates in Small Samples," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 208-16, April.
- Quintos, Carmela & Fan, Zhenhong & Phillips, Peter C B, 2001. "Structural Change Tests in Tail Behaviour and the Asian Crisis," Review of Economic Studies, Wiley Blackwell, vol. 68(3), pages 633-63, July.
- Jean-Marie Dufour, 2005.
"Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and non-standard asymptotics,"
CIRANO Working Papers
- Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
- DUFOUR, Jean-Marie, 2005. "Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics," Cahiers de recherche 2005-03, Universite de Montreal, Departement de sciences economiques.
- DUFOUR, Jean-Marie, 2005. "Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics," Cahiers de recherche 03-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Loretan, Michael Stanislaus & Kurz-Kim, Jeong-Ryeol, 2007. "A note on the coefficient of determination in regression models with infinite-variance variables," Discussion Paper Series 1: Economic Studies 2007,10, Deutsche Bundesbank, Research Centre.
- repec:ner:tilbur:urn:nbn:nl:ui:12-125712 is not listed on IDEAS
- Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
- Fama, Eugene F & French, Kenneth R, 1992. " The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-65, June.
- Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
When requesting a correction, please mention this item's handle: RePEc:eee:empfin:v:17:y:2010:i:2:p:180-194. 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.