Sequential Estimation of Hidden ARMA Processes by Particle Filtering—Part II

This is Part II of a series of two papers where we address sequential estimation of wide-sense stationary autoregressive moving average (ARMA) state processes by particle filtering. In Part I, we considered a state-space model where the state was an ARMA process of known order and where the parameters of the process could be known or unknown. In this paper, we extend our work from Part I by considering the same type of models, with the added complexity that the ARMA processes are now of unknown order. Instead of working on a scheme that first tracks the state by operating with different assumed models, and then selects the best model by using a predefined criterion, we present a method that directly estimates the state without the need of knowing the model order. We derive the transition density of the state for unknown ARMA model order, and propose a particle filter based on that density and the empirical Bayesian methodology. We demonstrate the performance of the proposed method with computer simulations and compare it with the methods from Part I.