You can use pole-zero plots of linear identified models to evaluate whether it might be useful to reduce model order. When confidence intervals for a pole-zero pair overlap, this overlap indicates a possible pole-zero cancellation.
For example, you can use the following syntax to plot a 1-standard deviation confidence interval around model poles and zeros.
If poles and zeros overlap, try estimating a lower order model.
Always validate model output and residuals to see if the quality of the fit changes after reducing model order. If the plot indicates pole-zero cancellations, but reducing model order degrades the fit, then the extra poles probably describe noise. In this case, you can choose a different model structure that decouples system dynamics and noise. For example, try ARMAX, Output-Error, or Box-Jenkins polynomial model structures with an A or F polynomial of an order equal to that of the number of uncanceled poles. For more information about estimating linear polynomial models, see Input-Output Polynomial Models.