Before moving to the actual question, I would like to emphasize on the following points (maybe they are obvious to some of you, but I still would like to list them, since they make the difference):
I don't have any reliable information on the input, thus I have only the measurements of the output $y(t)$.
I have only 1 set of recorded data, thus no repetitive measurements are in this case available.
Objective: Identifying a reliable transfer function model for this data in the frequency domain (e.g. rational fraction polynomial with numerator $B$ and denominator $A$)
Question: After obtaining a transfer function model, how does one validate this model and thus can be assured that it does not contain any systematic/modelling errors? Please, keep in mind the above 2 points!
To my limited experience, calculating the uncertainty of the transfer function residuals will be not possible, since the missing information on the input (and thus also not having the variance of the input). A second approach that I thought of is to do a 'simple' whiteness test of the residuals (sum of squares due to errors (SSE) or the R-square both mentioned in the Matlab manual), but is this approach even significant? I mean, sure... One obtains a result, but it's complex valued due to the data ($Y(k)$) which is also complex valued. Consequently, there is always an imaginary part which makes it fail the criterion (i.e. model is ok if SSE is close to 0). Any thoughts/solutions on this? Or am I mixing things up?
Any help, advise/guidance (tips) or references that I can consult in order to solve this issue is very much appreciated! Because I'm really lost and totally confused.