It appears that you are using the de jure date of the intervention as one of your predictors. You can add the other control variables and any needed ARIMA structure and any needed pulse indicators to complete the model. If you wish to identify the de facto date of the intervention while incorporating other control variables you may have to look for other software like AUTOBOX, which I have helped develop.
I am not an expert in SPSS so I suggest that you contact their support desk and ask them how to automatically detect the nature and form of needed (empirically detected) intervention variables while also automatically identifying any needed ARIMA structure and also while detecting the appropriate ADL/PDL for your user-suggested control variables.
MODIFIED TO RESPOND TO OP'S QUESTION ABOUT TRANSFER FUNCTION MODEL IDENTIFICAION:
In the case where y or x is non-stationary the suggested procedure is to difference each series according to it’s characteristics i.e. the appropriate differencing operator required for each series. In this case the appropriate differencing operator for y is a seasonal differencing operator while no differencing is need for x. A typical flaw in reasoning is often found on the web suggesting using the same differencing operator for both series and more incorrectly using just first differences rather than seasonal differences OR BOTH. The reason for the bad advice is often that it is easier to explain rather than doing it correctly i.e. using series specific differencing factors. Early computer implementation took the easy path of using the same differencing operator. A generally correct except for the error regarding the utilization of utilizing a common differencing operators is here https://onlinecourses.science.psu.edu/stat510/node/75/
The original citation for exactly how to deal with differencing operators is found at Section 5.3 of the 1976 seminal text by Box and Jenkins (Holden-Day) : TIME SERIES ANALYSIS Forecasting and Control ISBN 0=8162-1104-3 which details the possibility of unique differencing operators predicated upon the ARIMA model for each series.
The following advice from http://robjhyndman.com/uwafiles/fpp-notes.pdf has a cautionary but often ignored “if necessary” and a very important “Difference variables until all stationary” comment .
The following flow diagram may help:
In the case where y or x is non-stationary the suggested procedure is to difference each series according to it’s characteristics i.e. the appropriate differencing operator required for each series. In this case the appropriate differencing operator for y is a seasonal differencing operator while no differencing is need for x. A typical flaw in reasoning is often found on the web suggesting using the same differencing operator for both series and more incorrectly in this case using just first differences rather than seasonal differences. The reason for the bad advice is often that it is easier to explain rather than doing it correctly i.e. using series specific differencing factors. Early computer implementation took the easy path of using the same differencing operator. A generally correct except for the error regarding the utilization of utilizing a common differencing operators is here https://onlinecourses.science.psu.edu/stat510/node/75/
The original citation for exactly how to deal with differencing operators is found at Section 5.3 of the 1976 seminal text by Box and Jenkins (Holden-Day) : TIME SERIES ANALYSIS Forecasting and Control ISBN 0=8162-1104-3 which details the possibility of unique differencing operators predicated upon the ARIMA model for each series.
The following advice from http://robjhyndman.com/uwafiles/fpp-notes.pdf has a cautionary but often ignored “if necessary” and a very important “Difference variables until all stationary” comment .With this data that mean differ y seasonally (order 12) and don’t difference x.
In the case where y or x is non-stationary the suggested procedure is to difference each series according to it’s characteristics i.e. the appropriate differencing operator required for each series. In this case the appropriate differencing operator for y is a seasonal differencing operator while no differencing is need for x. A typical flaw in reasoning is often found on the web suggesting using the same differencing operator for both series and more incorrectly in this case using just first differences rather than seasonal differences. The reason for the bad advice is often that it is easier to explain rather than doing it correctly i.e. using series specific differencing factors. Early computer implementation took the easy path of using the same differencing operator. A generally correct except for the error regarding the utilization of utilizing a common differencing operators is here https://onlinecourses.science.psu.edu/stat510/node/75/
The original citation for exactly how to deal with differencing operators is found at Section 5.3 of the 1976 seminal text by Box and Jenkins (Holden-Day) : TIME SERIES ANALYSIS Forecasting and Control ISBN 0=8162-1104-3 which details the possibility of unique differencing operators predicated upon the ARIMA model for each series.
The following advice from http://robjhyndman.com/uwafiles/fpp-notes.pdf has a cautionary but often ignored “if necessary” and a very important “Difference variables until all stationary” comment .With this data that mean differ y seasonally (order 12) and don’t difference x.
A wise strategy is to prewhiten the user-specified stochastic (control) series in order to tentatively identify a possible transfer function the add the deteromistic control series . This is done in AUTOBOX simultaneously and may be done elsewhere. Then I would add the tentative ARIMA structure and then I would identify the deterministic series that you didn't suggest. This little trick is done via Intervention Detection procedures culminating after stepdown with a possibly useful model and an error sequence that is information free.
You appear to have a reasonable understanding of what to do. The degree of difficulty that may come into play is trying to get your current software to do these tasks.
http://www.autobox.com/stack/dpr-isf27.ppt slide 70 and on may provide some insight .
