The OE model structure is commonly used if the intended purpose is to model the system dynamics while ignoring the noise part. The output error structure does not comprise of a noise model, hence, you can apply an independence test criteria which represented by cross-correlation between the residuals and the past inputs using ‘resid’ matlab command for example.

the following book summarises all methods:

Digital Control Systems: Design, Identification and Implementation

By Ioan Doré Landau, Gianluca Zito 

The OE model structure is commonly used if the intended purpose is to model the system dynamics while ignoring the noise part. The output error structure does not comprise of a noise model, hence, you can apply an independence test criteria which represented by cross-correlation between the residuals and the past inputs using ‘resid’ matlab command for example.

resid, compare, FPE

Nuzaihan,

the main question is what is the intended use of your model? Test your model against those requirements regardless of how the noise is assumed to affect your model (e.g. output-error, equation-error etc.) That is far the best way of performing model validation in an application context. Unfortunately, however, we obtain models for the sake of, say, testing parameter estimation or structure selection algorithms. In that case, because it is not yet clear what is the intended use of the model, what is usually tested is the *estimator*... as, for instance, testing the whiteness of residuals has this "concealed" objective. There are lots of mdels that are useless and poor dynamically speaking and nevertheless have uncorrelated residuals.

So if you do NOT have any intended use for the model yet, and it is an output-error model, then: 1) make sure to include a noise model if you are going to use extended least squares, (alternatively you may try instrumental variables that does not require a noise model), and 2) test for uncorrelated residuals.