Sorry, I was wrong, you have to difference the dummy:
No, you can difference one series and leave another as it is.
What exactly is your indicator variable, an outlier like here:
Data A (Keep=x_i x t);
Retain e1 0 x1 0 x2 0 x_i_1 100;
Do t=-100 To 10000;
e=Rannor(0);
x=(0.02+0.8*x1-0.4*e1+e);
x_i=x_i_1+x;
e1=e;
x1=x;
x_i_1=x_i;
If t>0 Then Output;
End;
Run;
Data A;
Set A;
dummy=IfN(t>=6000 & t<=7500,1,0);
x_i_d=x_i-dummy*200; * <- something bad happens;
Run;
ODS Graphics On;
Proc Timeseries Data=A Plot=Series;
Var x_i_d x_i;
Run;
Proc Arima Data=A;
Title "Model 1: Has dent";
Identify Var=x_i_d (1) CrossCorr=dummy (1); * 1!!!!;
Estimate p=1 q=1 Input=dummy Method=ML;
Run;
Proc Arima Data=A;
Title "Model 2: No dent";
Identify Var=x_i (1);
Estimate p=1 q=1 Method=ML;
Run;
Title;
ODS Graphics Off;
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