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In this paper we consider a variety of procedures for numerical statisticalinference in the family of univariate and multivariate stable distributions. Inconnection with univariate distributions (i) we provide approximations byfinite location-scale mixtures and (ii) versions of approximate Bayesiancomputation (ABC) using the characteristic function and the asymptotic form ofthe likelihood function. In the context of multivariate stable distributions wepropose several ways to perform statistical inference and obtain the spectralmeasure associated with the distributions, a quantity that has been a majorimpediment in using them in applied work. We extend the techniques to handleunivariate and multivariate stochastic volatility models, static and dynamicfactor models with disturbances and factors from general stable distributions,a novel way to model multivariate stochastic volatility through time-varyingspectral measures and a novel way to multivariate stable distributions throughcopulae. The new techniques are applied to artificial as well as real data (tenmajor currencies, SP100 and individual returns). In connection with ABC specialattention is paid to crafting well-performing proposal distributions for MCMCand extensive numerical experiments are conducted to provide critical values ofthe "closeness" parameter that can be useful for further applied econometricwork.

Simple techniques for likelihood analysis of univariate and multivariate  stable distributions: with extensions to multivariate stochastic volatility  and dynamic factor models