I have a response time series(Y) & Input time series Xt & Zt. My only objective is to identify functional form Yt=f(Yt-1,Xt,Zt) where f(Yt-1,Xt,Zt) contains only lags of Yt , Xt & Zt as variables because I want to use this functional form as a constraint in an optimization model.
I used ARIMAX/Dynamic regression to do the same. But it gives a function form which have ARMA(p,q) of residuals also in f(Yt-1,Xt,Zt).
Having ARMA(p,q) of residuals in the functional form will not serve my purpose because my objective is to write f(Yt-1,Xt,Zt) in terms of lags of Yt, Xt & Zt only. And I assume i cannot just ignore ARMA(p,q) of residuals in the model when writing f(Yt-1,Xt,Zt). Please let me know if I can just drop it.
I tried linear regression but since this is time series data, residuals is having autocorrelation.
Other than ARIMAX & linear regression is there any model which will help me achieve my objective.