Tsionas, Mike (2012): Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models.

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Abstract
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite locationscale mixtures and (ii) versions of approximate Bayesian computation (ABC) using the characteristic function and the asymptotic form of the likelihood function. In the context of multivariate stable distributions we propose several ways to perform statistical inference and obtain the spectral measure associated with the distributions, a quantity that has been a major impediment in using them in applied work. We extend the techniques to handle univariate and multivariate stochastic volatility models, static and dynamic factor models with disturbances and factors from general stable distributions, a novel way to model multivariate stochastic volatility through timevarying spectral measures and a novel way to multivariate stable distributions through copulae. The new techniques are applied to artificial as well as real data (ten major currencies, SP100 and individual returns). In connection with ABC special attention is paid to crafting wellperforming proposal distributions for MCMC and extensive numerical experiments are conducted to provide critical values of the “closeness” parameter that can be useful for further applied econometric work.
Item Type:  MPRA Paper 

Original Title:  Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models 
Language:  English 
Keywords:  Univariate and multivariate stable distributions, MCMC, Approximate Bayesian Computation, Characteristic function 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C11  Bayesian Analysis: General 
Item ID:  40966 
Depositing User:  Mike Tsionas 
Date Deposited:  15. Sep 2012 21:04 
Last Modified:  14. Feb 2013 13:22 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/40966 