Data transformation before forecasting with ARIMA I have couple of questions in times series forecasting.


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*If the time series is nonstationary, should we make it to stationary for running auto.arima OR will this function automatically convert it? 

*How to optimise the auto.arima?

*If we take log of a time series to make it stationary, the forecasted values are in the log format. How do we convert them to the original scale?
 A: Be careful the presence of outliers will often cause the box-cox test to incorrectly suggest a power transformation that is uneeded . The box-cox test When (and why) should you take the log of a distribution (of numbers)? can often be misleading and should be used when the required assumptions are met i.e. no pulses , no seasonal pulses ; no level shifts and no trends in the residuals and of course no deterministic change points in error variance at particular points in time.
For more on this please see http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.469.7176&rep=rep1&type=pdf and in particular the section 7 on the "Effect of outliers and influential cases" 
A: 
If the time series is nonstationary, should we make it to stationary for running auto.arima OR will this function automatically convert it?

auto.arima will automatically convert it. arima, is so-called "auto-regression integrated moving average", there is a parameters "d" which is used for the order of first-differencing.

How to optimise the auto.arima?

auto.arima doing this automatically optimise using the stepwise algorithm.

If we take log of a time series to make it stationary, the forecasted values are in the log format. How do we convert them to the original scale?

If you manually log the time series, then you should manually convert the forecast values to the original scale.
