I am having some issues with differencing using auto.arima when also
specifying an xreg dataframe.
The xreg dataframe contains dummy variables that specify time periods that
had a promotion running.
When I model diff(y) with order (1,0,1), the coefficients for these dummy
variables are very different than when I model y with order=(1,1,1). I
think when modeling diff(y) the coefficients represent the % change from
week to week (since the response is first logged) and I may be having issues
trying to run a dummy variable over consecutive periods since the promotion
is probably not causing increases in % changes at each time period. But
when modeling y with order (1,1,1), it allows me to use the dummy variable
over consecutive periods and appears meaningful.
Does anyone have any insight as to why this is happening?
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