Folks,
  This is more of a stat question than an R question.

Apologies in advance!

Suppose I fit an AR(1) to a time-series and also fit an AR(1) to the logs of the same time-series and then simulate future paths.

In my case I see a big difference in the resulting paths. If I simulate thousands of paths under each scenario (exponentiating the results from the log-fit) and take the "mean" path for each I see a divergence. The average path from log-fit is increasing relative to the average path of the base fit.

My guess is that there is a simple computation that would allow me to compare the two analytically but I just haven't been able to find it.

Thanks for your time,
KW

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