When identifying a transfer function model with multiple input variables, the cross-correlation functions can be misleading if the input series are correlated with each other. Any dependencies among two or more input series will confound their cross-correlations with the response series.

The prewhitening technique assumes that the input variables do not depend on past values of the response variable. If there is feedback from the response variable to an input variable, as evidenced by significant cross-correlation at negative lags, both the input and the response variables need to be prewhitened before meaningful cross-correlations can be computed.

PROC ARIMA cannot handle feedback models. The STATESPACE and VARMAX procedures are more appropriate for models with feedback.