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If I apply ARMA on a stationary differentiated time series and want to make forecasts with this model, the forecast will be on the differentiated values. I need the values to be non-differentiated, is it possible?

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If you forecast $\Delta X_t$ then to get the forecast of $X_t$ simply sum up the differences:

\begin{align*} \hat{X}_{t+1}&=\hat{\Delta X_{t+1}}+X_t\\ \hat{X}_{t+2}&=\hat{\Delta X_{t+2}}+\hat{\Delta X_{t+1}}+X_t\\ ... &\\ \hat{X}_{t+h}& =\hat{\Delta X_{t+h}}+\Delta \hat{X}_{t+h-1}+...+\hat{\Delta X_{t+1}}+X_t \end{align*}

where we assume that $X_t$ is the last known in-sample value.

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  • $\begingroup$ Thanks! That is what I thought! Is there a easy way of doing this in r? I'm using rugarch for the forecast! $\endgroup$ – Confused student Nov 28 '13 at 17:10
  • $\begingroup$ Use function cumsum. If dx is your forecasted differences then the level forecast is cumsum(dx)+xt. $\endgroup$ – mpiktas Nov 28 '13 at 17:56

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