Bayesian estimation of polynomial moving average models with unknown degree of nonlinearity

Various real world phenomena such as optical communication channels, power amplifiers and movement of sea vessels exhibit nonlinear characteristics. The nonlinearity degree of such systems is assumed to be known as a general intention. In this paper, we contribute to the literature with a Bayesian estimation method based on reversible jump Markov chain Monte Carlo (RJMCMC) for polynomial moving average (PMA) models. Our use of RJMCMC is novel and unique in the way of estimating both model memory and the nonlinearity degree. This offers greater flexibility to characterize the models which reflect different nonlinear characters of the measured data. In this study, we aim to demonstrate the potentials of RJMCMC in the identification for PMA models due to its potential of exploring nonlinear spaces of different degrees by sampling.