ndiffs returns maximal or minimal differencing order?

[j-adamczyk]

Describe the question you have

As far as I understand, we want to avoid over-differencing, i.e. don't difference if we don't have to. Looking at ndiffs functions docs, it states:

Will select the maximum value of ``d`` for which the time series is judged stationary by the statistical test.

Shouldn't this be "minimal" value instead? If it's maximal, if a time series is already stationary at d=0, and is stationary after differencing d=1, maximal means that we differentiate when we don't have to.

Looking at the code, I'm also not sure if this returns maximal order: https://github.com/alkaline-ml/pmdarima/blob/15919ef6/pmdarima/arima/utils.py#L196. The while loop will break when dodiff is False, which is true when p-value is lower than alpha. KPSS test decides whether the series needs further differencing. So if I understand correctly, this will break as soon as the series does not need further differencing (i.e. is already stationary), so it would choose the minimal d value.

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