Abstract:

Markov chain Monte Carlo (MCMC) methods for the parameter estimation of α-stable distributions have good performance, but an improper choice of proposal distributions can often lead to unexpected results. Aiming at the difficulties to choose an effective proposal distribution, a novel method based on adaptive Metropolis (AM) algorithm is proposed for nonsymmetric αstable distributions. The method uses the full history (cumulated so far) of the chain to tune the covariance of the proposal distribution suitably. This adaptation strategy can approach an approximation of the target distribution, which increases the efficiency of the simulation. Theoretic analysis and simulation results show that this method can not only estimate the four parameters of  α-stable distributions, but also perform very accurately and robustly.