Estimating the parameters for the Box-Jenkins models is a quite complicated non-linear estimation problem. For this reason, the parameter estimation should be left to a high quality software program that fits Box-Jenkins models. Fortunately, many commerical statistical software programs now fit Box-Jenkins models.
The main approaches to fitting Box-Jenkins models are non-linear least squares and maximum likelihood estimation.
Maximum likelihood estimation is generally the preferred technique. The likelihood equations for the full Box-Jenkins model are complicated and are not included here. See (Brockwell and Davis, 1991) for the mathematical details.
Model Estimation Example
The Negiz case study shows an example of the Box-Jenkins model-fitting.