Abstract
In the present paper, we propose a unified approach to order determination of the process and noise dynamics by the order test statistics which is 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 it enables us to determine both orders of the process and noise dynamics in a unified manner, while the ordinary statistics based on the instrumental variables method are fluctuating for those models, which inevitably causes the separate order determination of the process and noise dynamics. The proposed statistics is efficiently evaluated by a newly derived recursive algorithm. On Monte Carlo simulations we confirmed the validity of our approach.
