Is the variance changing in this

[noetsi]

If variance changes over time it is suggested you log the data. I can never figure out if the variance is changing. This is the raw data (if it matters the data ends up being a seasonal arima which differences). The ARIMA that was chosen by auto.arima (when I did not log the data) was ARIMA(0,1,1)(1,0,0)[12]

If its suggested that I log the data, how do I log it and convert it back when I do the forecast statement in R (in the library forecast ideally)?

 

[noetsi]

Is there a test for changing variance over the course of the time series. I know there is a chi square test for changing variance, but I don't know how to apply this to a time series that changes all the time.

It has been pointed out to me that a time series can change over time or with the mean of a series. I need test for both. Can one even do ARIMA if the variance changes over time or do you have to use ARCH/GARCH models.

I think those are beyond my IQ level