Bayesian inferences and forecasting in bilinear time series models

Abstract

In this paper, we propose a Bayesian approach to the analysis of bilinear time series which is an extension of Broemeling and Shaarawy's work (1988) on linear time series. The conjugate prior for parameters is used to derive the predictive distribution and the marginal posterior distribution of the bilinear parameters, by which we make inferences about the parameters and for a future observation. Our results are illustrated using the Wolf sunspot numbers from Box and Jenkins (1976) and are compared with a linear time series.