Bayesian analysis of fractionally integrated ARMA with additive noise

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Abstract
A new sampling‐based Bayesian approach for fractionally integrated autoregressive moving average (ARFIMA) processes is presented. A particular type of ARMA process is used as an approximation for the ARFIMA in a Metropolis–Hastings algorithm, and then importance sampling is used to adjust for the approximation error. This algorithm is relatively time‐efficient because of fast convergence in the sampling procedures and fewer computations than competitors. Its frequentist properties are investigated through a simulation study. The performance of the posterior means is quite comparable to that of the maximum likelihood estimators for small samples, but the algorithm can be extended easily to a variety of related processes, including ARFIMA plus short‐memory noise. The methodology is illustrated using the Nile River data. Copyright © 2003 John Wiley & Sons, Ltd.