I have a model fitted with
auto.arima, the model is ARIMA(0,1,0)x(0,1,0) with seasonal period 6. The data is bi-monthly so there is an annual seasonality. There is only one regressor indicating an intervention (dummy).
Then I used this model to old data to see what would have happened if the intervention would have done since and earlier period, using the model and forecast from an earlier data. The thing I do not understand yet is that if I suppose the intervention only occur in one period, the series only differ in this period. Therefore, there is no persistence on the intervention.
As I understand, the model has ARIMA errors. The error in the intervention period should change and so there should be an effect in the next periods when using forecast to predict futures values. If the intervention occurs in only one period, why in the forecast the intervention does not affect futures predictions?
The code I am using is
model1<-auto.arima(ts,xreg = X.ts)
X.ts is a
ts object with
0 and a period with intervention.
Then I used
model2<-Arima(Xold, xreg= X.ts.old, model=model1)
So I used the first model on earlier data to make the following
So I am trying to show what would have been expected from an earlier period (the forecast) if the intervention would have started earlier.
The thing I do not understand yet is that for instance
forecast(model2, xreg=cbin(c(0,1,1,1,0...)) forecast(model2, xreg=cbin(c(0,1,1,1,1...))
only differ in the periods the
xreg differ, with no persistence of these differences. I did not expect this, why is that?