I estimate a variable x from a differenced equation such that x is attained in its first differences. But now I need this variable in its levels. Could someone please suggest me how to do so? If I need to compute integrals of differenced X, how may I do so in excel, stata eviews?
This is straightforward. You need the original undifferenced series up to a certain point. If d is the order of differencing, you add the original value to the difference at a distance d from it to obtain the original series at that point. That is
Delta_d(X_t) = X_t - X_(t-d)
Therefore
X_(t-d) = Delta_d + X_(t)
The issue is the variable is an estimated one. There exists no original series
If there is no original series I am sorry there is nothing anybody can do about it. If the order of differencing is one, a value of the original series can be arbitrarily fixed and the original data generated. The original data so obtained will bear a constant difference from the actual original series.
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