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Is it possible to fit an ARIMA under a restriction that bounds the minimum to positive values? I'm using Minitab.

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    $\begingroup$ Transform your data to the whole real line, do the forecasts, and back-transform. $\endgroup$ – Rob Hyndman Oct 19 '12 at 23:10
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In Minitab, there is no option to restrict the forecasts to positive using ARIMA. Probably you need to consider doing log transformation before forecast and back transform after that as mentioned in the comment above.

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