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Indirect Estimation of α-Stable Distributions and Processes

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Marco J. Lombardi
Giorgio Calzolari

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Abstract

The α-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 behaviour of the tails. Estimation difficulties have however hindered its diffusion among practitioners. Since stably distributed random numbers can be produced thoroughly, we propose an indirect estimation approach which uses a skew-t distribution as auxiliary model. The properties of this approach are assessed in a detailed simulation study. Copyright Royal Economic Society 2008

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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1368-423X.2008.00234.x
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Article provided by Royal Economic Society in its journal Econometrics Journal.

Volume (Year): 11 (2008)
Issue (Month): 1 (03)
Pages: 193-208
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Handle: RePEc:ect:emjrnl:v:11:y:2008:i:1:p:193-208

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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.:
  1. 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 "G. Parenti". [Downloadable!]
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  2. Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004. "Constrained Indirect Estimation," Review of Economic Studies, Blackwell Publishing, vol. 71(4), pages 945-973, October. [Downloadable!] (restricted)
  3. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October. [Downloadable!]
  4. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De. [Downloadable!] (restricted)
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  5. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
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  1. 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 "G. Parenti". [Downloadable!]
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