Estimation of Stable Distributions by Indirect Inference

This article deals with the estimation of the parameters of an α-stable distribution by the indirect inference method with the skewed-t distribution as an auxiliary model. The latter distribution appears as a good candidate for an auxiliary model since it has the same number of parameters as the α-stable distribution, with each parameter playing a similar role. To improve the properties of the estimator in finite sample, we use a variant of the method called Constrained Indirect Inference. In a Monte Carlo study, we show that this method delivers estimators with good properties in finite sample. In particular they are much more efficient than two other prevalent methods based on the characteristic function and the empirical quantiles. We provide an empirical application to hedge fund returns.