Advanced Search
MyIDEAS: Login to save this article or follow this journal

Bayesian inference for [alpha]-stable distributions: A random walk MCMC approach

Contents:

Author Info

  • Lombardi, Marco J.

Abstract

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.)

Download Info

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.
File URL: http://www.sciencedirect.com/science/article/B6V8V-4J6NGHT-1/2/970efecb95ce2f85af177f67a7f81543
Download Restriction: Full text for ScienceDirect subscribers only.

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.

Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 51 (2007)
Issue (Month): 5 (February)
Pages: 2688-2700

as in new window
Handle: RePEc:eee:csdana:v:51:y:2007:i:5:p:2688-2700

Contact details of provider:
Web page: http://www.elsevier.com/locate/csda

Related research

Keywords:

Other versions of this item:

References

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.:
as in new window
  1. Tsionas, Efthymios G., 1998. "Monte Carlo inference in econometric models with symmetric stable disturbances," Journal of Econometrics, Elsevier, Elsevier, vol. 88(2), pages 365-401, November.
  2. 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".
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Szymon Borak & Adam Misiorek & Rafał Weron, 2010. "Models for Heavy-tailed Asset Returns," SFB 649 Discussion Papers SFB649DP2010-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Adam Misiorek & Rafal Weron, 2010. "Heavy-tailed distributions in VaR calculations," HSC Research Reports, Hugo Steinhaus Center, Wroclaw University of Technology HSC/10/05, Hugo Steinhaus Center, Wroclaw University of Technology.
  3. Dominicy, Yves & Veredas, David, 2013. "The method of simulated quantiles," Journal of Econometrics, Elsevier, Elsevier, vol. 172(2), pages 235-247.
  4. 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".
  5. Marco Lombardi & Giorgio Calzolari, 2006. "Indirect estimation of alpha-stable stochastic volatility models," Econometrics Working Papers Archive wp2006_07, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  6. Peters, G.W. & Sisson, S.A. & Fan, Y., 2012. "Likelihood-free Bayesian inference for α-stable models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(11), pages 3743-3756.
  7. Marco J. Lombardi & Giorgio Calzolari, 2004. "Indirect estimation of alpha-stable distributions and processes," Econometrics Working Papers Archive wp2004_07, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  8. Strid, Ingvar, 2010. "Efficient parallelisation of Metropolis-Hastings algorithms using a prefetching approach," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 54(11), pages 2814-2835, November.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

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: (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.