Particle filtering of ARMA processes of unknown order and parameters

This paper considers inference on the widely used state-space models described by hidden ARMA state processes of unknown order observed via non-linear functions of the states. We propose a particle filtering method for sequentially inferring the unknown ARMA time-series by Rao-Blackwellization of all the static unknowns. Our method does not rely either on any assumption on the model order or on the static ARMA and state innovation parameters. Consequently, when the ARMA model order is unknown, it can be used without a follow-up model selection procedure. Extensive simulation results validate the proposed method across different ARMA models.