I want to do a rolling window forecast on a time series but it seems the series is white noise ARIMA (0,0,0) with non-zero mean. But when I difference the dataset and model it with an ARIMA(0,1,1) I get a really good forecast compared to the ARIMA (0,1,0).
Why, and is the differenced forecast not valid?
Red Line = ARIMA (0,1,1) and Blue line = ARIMA (0,0,0)
The Arima(0,0,0) and Arima(0,1,1) fitted on a rolling window and same original dataset with the below out-of sample forecast results. Should the forecasts not be equal in the case of white noise?