Fast algorithm for identification of an ARX model and its order determination

In this paper, we present a fast algorithm for fitting ARX models and determining their orders from the covariance and cross-covariance information of input and output processes. Ascending and descending order-update recurrences will be presented first for fitting an ARX model. These recurrences will be applied to the order determination of ARX models based on Akaike´s information criterion. This algorithm reduces the computation required for fitting an ARX model (m, n) and its associated order determination to a number of operations proportional to 0[ (m + n)²], compared to the usual Cholesky decomposition method which requires a number of operations proportional to 0[(m + n)⁴]. Some numerical examples, as well as the Pascal source programs, are presented to illustrate the efficiency of this algorithm.