Extract shift from ARMA process

[user24feb]

Hello,

I simulated an ARMA 1,1 process and added a level shift. How can I get closer to the actual parameter estimates of the model if a shift is included?

Data A (Keep=x_int x t);
  Retain e1 0 x1 0 x_int_1 500;  
  Do t=-100 To 10000;
    e=Rannor(1);
	x=(0.02+0.8*x1-0.4*e1+e); * create ARMA 1,1;
	x_int=x_int_1+x; * integrate;
	e1=e;
	x1=x;
	x_int_1=x_int;
	If t>0 Then Output;
  End;
Run;

Data A;
  Set A;
  dummy=IfN(t>=6000 & t<=7500,1,0);
  x_int_d=x_int-dummy*200; * create shift;
Run;

ODS Graphics On;
Proc Timeseries Data=A Plot=Series;
  Var x_int_d x_int;
Run;
ODS Graphics Off;

Proc Arima Data=A;
  Title "Model 1: With shift";
  Identify Var=x_int_d (1) CrossCorr=dummy;
  Estimate p=1 q=1 Noint Input=dummy Method=ML;
Run;
Proc Arima Data=A;
  Title "Model 2: No shift";
  Identify Var=x_int (1);
  Estimate p=1 q=1 Method=ML;
Run;

Thanks&kind regards

[alexchien · Accepted solution]

you have to diff the dummy too.

Proc Arima Data=A;
Title "Model 1: With shift";
Identify Var=x_int_d (1) CrossCorr=dummy(1);
Estimate p=1 q=1 Noint Input=dummy Method=ML;
Run;