1. The arima\estimate method will return to you the data on the original scale. That is if you do:
Mdl = arima(1,1,1);
Mdl = estimate(Mdl,data);
res = infer(Mdl,data);
foreValues = forecast(Mdl,1,'Y0',data','E0',res)
Your forecasted data will be on the same scale as data and not the differenced data. The difference operator is just applied and you have the model you wrote above, but are simply returned y(k),y(k+1),...
2. The residual e(k-1) is he last value in the variable res above. That is, if you pass 'E0' to the forecast method it will use the residuals which were infered from the model and data.
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