Fast Bayesian Estimation for VARFIMA Processes with Stable Errors

Abstract

We present an approach via a multivariate preconditioned conjugate gradient (MPCG) algorithm for Bayesian inference for vector ARFIMA models with sub-Gaussian stable errors. This approach involves solution of a block-Toeplitz system, and treating the unobserved process history and the underlying positive stable process as unknown parameters in the joint posterior. We use Gibbs sampling with the Metropolis-Hastings algorithm. We illustrate our approach on time series of daily average temperatures measured over several years at different U.S. cities.