Bayesian inference for [alpha]-stable distributions: A random walk MCMC approach
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, given that 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. The absence of the density function in a closed form and the associated estimation difficulties have however hindered its diffusion among practitioners. In this paper I introduce a novel approach for Bayesian inference in the setting of alpha-stable distributions that resorts to a FFT of the characteristic function in order to approximate the likelihood function; the posterior distributions of the parameters are then produced via a random walk MCMC method. Contrary to the other MCMC schemes proposed in the literature, the proposed approach does not require auxiliary variables, and so it is less computationally expensive, especially when large sample sizes are involved. A simulation exercise highlights the empirical properties of the sampler; an application on audio noise data demonstrates how this estimation scheme performs in practical applications.
(This abstract was borrowed from another version of this item.)
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.:
- Marco J. Lombardi & Simon J. Godsill, 2004. "On-line Bayesian estimation of AR signals in symmetric alpha-stable noise," Econometrics Working Papers Archive wp2004_05, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
- Tsionas, Efthymios G., 1998. "Monte Carlo inference in econometric models with symmetric stable disturbances," Journal of Econometrics, Elsevier, vol. 88(2), pages 365-401, November.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:51:y:2007:i:5:p:2688-2700. 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: (Dana Niculescu)
If references are entirely missing, you can add them using this form.