A Unified Approach to Determination of Process and Noise Order

Abstract This paper proposes a unified approach to order determination of the process and noise dynamics by the order test statistics developed on a new concept of model correlation residuals. The statistics is not fluctuating even for models of order exceeding the process order so that both orders of the process and noise can be determined in a unified manner, whereas the ordinary statistics based on the instrumental variables method are fluctuating for those model, which inevitably cause the separate order determination of the process and noise. The proposed statistics is efficiently evaluated by a newly derived recursive algorithm. The validity of our approach was confirmed on Monte Carlo simulations.