Indirect estimation of alpha-stable distributions and processes
The alpha-stable family of distributions constitutes a generalization of the Gaussian distribution, allowing for asymmetry and thicker tails. Its practical usefulness is coupled with a marked theoretical appeal, as it stems from a generalized version of the central limit theorem in which the assumption of the finiteness of the variance is replaced by a less restrictive assumption concerning a somehow regular behavior of the tails. Estimation difficulties have however hindered its diffusion among practitioners. Since simulated values from alpha-stable distributions can be straightforwardly obtained, the indirect inference approach could prove useful to overcome these estimation difficulties. In this paper we provide a description of how to implement such a method by using a skew-t distribution as an auxiliary model. The indirect inference approach will be introduced in the setting of the estimation of the distribution parameters and then extended to linear time series models with alpha-stable disturbances. The performance of this estimation method is then assessed on simulated data. An application on time-series models for the inflation rate concludes the paper.
|Date of creation:||01 Jun 2004|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: +39 055 2751500
Fax: +39 055 4223560
Web page: http://www.disia.unifi.it/
More information through EDIRC
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.:
- Gourieroux, C & Monfort, A & Renault, E, 1993.
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De.
- Gallant, A. Ronald & Tauchen, George, 1996.
"Which Moments to Match?,"
Cambridge University Press, vol. 12(04), pages 657-681, October.
- Casarin, Roberto, 2003. "Bayesian Inference for Mixtures of Stable Distributions," Economics Papers from University Paris Dauphine 123456789/6326, Paris Dauphine University.
- Marco J. Lombardi, 2004.
"Bayesian inference for alpha-stable distributions: a random walk MCMC approach,"
Econometrics Working Papers Archive
wp2004_11, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
- Lombardi, Marco J., 2007. "Bayesian inference for [alpha]-stable distributions: A random walk MCMC approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2688-2700, February.
- Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389.
- repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
- Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004.
"Constrained Indirect Estimation,"
Review of Economic Studies,
Oxford University Press, vol. 71(4), pages 945-973.
When requesting a correction, please mention this item's handle: RePEc:fir:econom:wp2004_07. 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: (Francesco Calvori)
If references are entirely missing, you can add them using this form.