Estimation of the Bivariate Stable Spectral Representation by the Projection Method

A method of estimating the spectral representation of a generalized bivariate stable distribution is presented, based on a series of maximum likelihood (ML) estimates of the stable parameters of univariate projections of the data. The corresponding stable spectral density is obtained by solving a quadratic program. The proposed method avoids the often arduous task of computing the multivariate stable density, relying instead on the standard univariate stable density. The paper applies this projection procedure, under the simplifying assumption of symmetry, to simulated data as well as to foreign exchange return data, with favorable results. Kanter projection coefficients governing conditional expectations are computed from the estimated spectral density. For the simulated data these compare well to their known true values.