Optimal Calculation of Residuals for ARMAX Models with Applications to Model Verification

Residual tests for sufficient model orders are based on the
assumption that prediction errors are white when the model is
correct. If an ARMAX system has zeros in the MA part which are
close to the unit circle, then the standard predictor can have
large transients. Even when the correct model is used there will
be large correlations in the transient phase. In this case the
standard residual tests are therefore not suitable. A new method
based on backforecasting is therefore developed. Simulation and
analysis shows that the new method gives the right answer where
the standard method is misleading.