Bayesian wavelet analysis of autoregressive fractionally integrated moving-average processes

Long memory processes are widely used in many scientific fields, such as economics, physics and engineering. In this paper we describe a wavelet-based Bayesian estimation procedure to estimate the parameters of a general Gaussian ARFIMA (p,d,q)(p,d,q), autoregressive fractionally integrated moving average model with unknown autoregressive and moving average parameters. We employ the decorrelation properties of the wavelet transforms to write a relatively simple Bayes model in the wavelet domain. We use an efficient recursive algorithm to compute the variances of the wavelet coefficients. These depend on the unknown characteristic parameters of the model. We use Markov chain Monte Carlo methods and direct numerical integration for inference. Performances are evaluated on simulated data and on real data sets.