A Box-Jenkins method that is asymptotically globally convergent for open loop data

An algorithm for the identification of a multi-input single-output (MISO) Box-Jenkins model is developed. The method consists of several simple steps: first a high order ARX model is estimated; then the process model is calculated using the so-called Steiglitz-McBride iteration on the filtered input-output data; and finally the disturbance model is calculated by estimating an ARMA model of the output error residual. It can be proven that the Steiglitz-McBride iteration for the process model part is asymptotically globally convergent. The proposed method outperforms a standard Box-Jenkins method in simulation examples.