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|
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- 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".
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- 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.
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Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
- 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.
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