ARIMA with independent variables I'm a Data Scientist, but new to time series methods.  I primarily use SPSS, but I'm familiar with R. 
I have read Rob's blog, various books, and taken a few courses.  I have a couple of outstanding questions for which I'm seeking assistance: 


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*I have independent variables that I would like to use as predictors - I have used first differencing to make them "stationary"; it seems to have worked. Is this an appropriate step.  Also, it seems that SPSS (or auto.arima in R) will do this step for you.  (also: SPSS doesn't have the adf.test function for stationarity, so I have to export my data to R to do that)

*All of my predictors had an ACF/PCF which suggested a first-order AR term.  The dependent variable was an AR(3) process.  However, when I used the auto.arima function (or SPSS expert modeler), none of the independent variables were significant.  However, if I manually specified the transfer function in SPSS, then several of the lagged predictors did become significant.  How is that possible?  

*I'm not sure if I'm missing something in this process.  It seems that if my Y is stationary, and my x's (independents) are stationary, then the modeling should pick up significant predictors (if there are any).   
I can post raw data / SPSS output if that would help. 
Thanks for anyone who takes the time to respond! 
EDIT - adding graphs and data 
This is the ACF Plot of the dependent variable

This is the DV sequence plot after first-order differencing to remove trend

This is the ACF plot of the IV (predictor) showing a likely AR(1) process

This is the sequence plot after first-order differencing to remove trend

SPSS Output using the ARIMA "Expert Modeler".  The model found an AR(3) process for the DV (revenue) but none of the other 3 predictor variables were found to be statistically significant*

SPSS Output using a custom Transfer Model.  If, instead, I customize the ARIMA model I get significant results.  The same covariates were used as in the model above.  The only difference is that I specified the numerator of the transfer function as "1", to be consistent with the ACF plots and their respective AR process

Below are the windows where I specified the transfer function.  There are two - one where you specify the transfer function of the model (for the DV) and a second window where you can specify the transfer function parameters for each individual IV


so my question is... what am I doing wrong.  Or have I misundertood something about modeling indpendent variables in an ARIMA process?
I'm not sure if I can upload the raw data, but I'm happy to share it if anyone would like to run the numbers themselves.
 A: post your data in a csv format . If you can't then email it to me and I will take a look . In general the nature of X or Y ( in terms of stationarity ) has nothing whatsoever to do with the functional form relating X to Y . However when one identifies the form of the relationship one needs to transform X and Y appropriately This is discussed here   Why is prewhitening important?… .   Another discussion Transfer function in forecasting models - interpretation might also help.
EDITED AFTER RECEIPT OF DATA:
I took your 31 monthly values for the 4 series and introduced them to AUTOBOX , a piece of time series software that I have helped to develop. It developed pre-whitening models for all 4 series and developed the following model  .
Not terribly different from your SPSS model but it did detect 3 seasonal pulses which are very important in making a useful forecast.
The residual from the model are here and a table of forecasts is presented here  including the uncertainty in the three predictor series.
The Actual/Fit and Forecast is here .... 
