[ENH] ensure Prophet can deal with PeriodIndex

[fkiraly]

Currently, Prophet errors out when given data frames with PeriodIndex, due to the interfaced facebook prophet not liking that index (and catch statements in our interface).

We may want to add some intermediate functionality to enable Prophet to also deal with PeriodIndex? In that case, I'd simply convert it to the first time stamp in a period, then apply Prophet as is, and at the end convert back to PeriodIndex.

Good first issue, the one non-obvious thing perhaps is that the places to look at includes the _ProphetAdapter class as well.

[aiwalter]

back in the days we have decided to accept only pd.DatatimeIndex and not do the conversion as not for all freq values you can convert back and forth without loss of freq information. I even opened 2 bug issues for this on pandas GitHub which are still open:

pandas-dev/pandas#38914
pandas-dev/pandas#38885

So we might have to implement a custom dummy index conversion:

[fkiraly]

back in the days we have decided to accept only pd.DatatimeIndex and not do the conversion

But already our example datasets violate this input assumption, e.g., load_longley used above.
This is programmed to cause user frustration...

[aiwalter]

yes, we should actually open an issue at prophet about this

[fkiraly]

with last release over a year ago? Can try, but sounds unlikely...
We'll probably need to find a way to work around it