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.