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Likelihood-free Bayesian inference for α-stable models

Author

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  • Peters, G.W.
  • Sisson, S.A.
  • Fan, Y.

Abstract

α-stable distributions are utilized as models for heavy-tailed noise in many areas of statistics, finance and signal processing engineering. However, in general, neither univariate nor multivariate α-stable models admit closed form densities which can be evaluated pointwise. This complicates the inferential procedure. As a result, α-stable models are practically limited to the univariate setting under the Bayesian paradigm, and to bivariate models under the classical framework. A novel Bayesian approach to modelling univariate and multivariate α-stable distributions is introduced, based on recent advances in “likelihood-free” inference. The performance of this procedure is evaluated in 1, 2 and 3 dimensions, and through an analysis of real daily currency exchange rate data. The proposed approach provides a feasible inferential methodology at a moderate computational cost.

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  • Peters, G.W. & Sisson, S.A. & Fan, Y., 2012. "Likelihood-free Bayesian inference for α-stable models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3743-3756.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:11:p:3743-3756
    DOI: 10.1016/j.csda.2010.10.004
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    2. Kobayashi, Genya, 2014. "A transdimensional approximate Bayesian computation using the pseudo-marginal approach for model choice," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 167-183.
    3. Calzolari, Giorgio & Halbleib, Roxana & Parrini, Alessandro, 2014. "Estimating GARCH-type models with symmetric stable innovations: Indirect inference versus maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 158-171.
    4. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    5. Koblents, Eugenia & Míguez, Joaquín & Rodríguez, Marco A. & Schmidt, Alexandra M., 2016. "A nonlinear population Monte Carlo scheme for the Bayesian estimation of parameters of α-stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 57-74.
    6. Paola Stolfi & Mauro Bernardi & Lea Petrella, 2018. "The sparse method of simulated quantiles: An application to portfolio optimization," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 375-398, August.

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