Bayesian prediction for vector ARFIMA processes

Abstract

We provide explicit formulae for the joint predictive distribution of a Gaussian vector autoregressive fractionally integrated moving average (VARFIMA) process and describe a Bayesian method for its feasible evaluation. Inference for the parameters in the Bayesian framework is based on the joint posterior distribution of the model parameters using the exact likelihood function, as described in Ravishanker and Ray [Australian Journal of Statistics 23 (1997) 295-312]. Markov chain Monte Carlo methods are used to generate samples from the joint predictive distributions of unknown future realizations conditional on the observed data. The means or medians of the sampled predictions provide point forecasts of the future realizations, while the sample prediction quantiles provide prediction intervals. The approach is illustrated using sea surface temperatures along the California coast at three locations. © 2002 International Institute of Forecasters. Published by Elsevier Science B.V. All rights reserved.