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I would like to know if the ARIMAx model is considered a transfer function model. If the answer is no, further explanation on what are differences would be appreciated.

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Yes, Hyndman has a brief explanation of the subject here. ARIMAX is a transfer model $$y_t=\frac {\beta(B)} {v(B)} x_t+\frac{\theta(B)}{\phi(B)}z_t$$ where $x_t$ is contemporaneous exogenous variables and $\beta(B)=\beta$ is a simple coefficient matrix. The transfer function approach would have $\beta(B)$ with a set of possibly lagged exogenous variables.

A thing to be aware of is that sometimes by ARIMAX people, including Hyndman himself, call a different special case of transfer function model that is referred to as regARIMA in MATLAB or regression with ARIMA errors. A case in point is SARIMAX in Python statsmodels. The regression with arima errors model is: $$y_t=\beta x_t+\frac{\theta(B)}{\phi(B)}z_t$$

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  • $\begingroup$ today i posted a question on a similar topic (i.e. regression with GARCH error term), I provide the link here do you know the answer? Thanks in advance $\endgroup$ – Fr1 Aug 5 at 19:52
  • $\begingroup$ Thank you for your great answer @Aksakal. $\endgroup$ – Stats Panda Aug 5 at 21:45

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