The Box–Jenkins Steiglitz–McBride algorithm

An algorithm for identification of single-input single-output Box–Jenkins models is presented. It consists of four steps: firstly a high order ARX model is estimated; secondly, the input–output data is filtered with the inverse of the estimated disturbance model; thirdly, the filtered data is used in the Steiglitz–McBride method to recover the system dynamics; in the final step, the noise model is recovered by estimating an ARMA model from the residuals of the third step. The relationship to other identification methods, in particular the refined instrumental-variable method, are elaborated upon. A Monte Carlo simulation study with an oscillatory system is presented and these results are complemented with an industrial case study. The algorithm can easily be generalized to multi-input single-output models with common denominator.