I am examining monthly road accident counts over the last 25 years. I have created an ARIMA model in R using rainfall and temperature deviations from the long-term monthly average as exogenous variables, to see how these weather effects impact on the number of road collisions.
Now, I am looking to utilise the model to investigate what collisions would have looked like in those 25 years if the weather was normal, i.e. zero deviation in January from the long-term January average, zero deviation in February from the long-term February average, etc. Basically, how do I remove the impact of my weather variables from the collision time series?
My thinking is that I create an ARIMA forecast in which I replace the 'real' exogenous weather variables with 'normalised' weather variables (zero deviation from long-term averages, so essentially a time series of all zeros).
Is this approach sound / logical?