[REF] Move constructor helpers to EA Mixin classes

[jbrockmendel]

After this:

• Tests
• Comparisons
• Tests
• Deal with the fact that DatetimeIndex caches ranges, only feasible because of immutability
• Tests!
• formatting/__repr__ methods
• Teeeeeests
• Double-check docstring accuracy

[jorisvandenbossche]

Are there methods left that can rather simply be moved?

[jbrockmendel]

Are there methods left that can rather simply be moved?

For the arithmetic/comparison methods (and their dependencies) that I've mostly been focused on, not really. Most of what's left either a) dispatches to the base Index class and so is non-trivial, or b) requires more of __new__ to be ported (DatetimeIndexOpsMixin.shift passes start and end kwargs to the constructor which are not currently handled).

There are a few more that can be moved with Index-wrapping left in the Index subclasses. DatetimeIndex.to_period, PeriodIndex.to_timestamp, ...

There are a few that would be simple but I'm not yet sure if they should be moved: inferred_type, is_all_dates, is_type_compatible, PeriodIndex.tz_convert, PeriodIndex.tz_localize

[jbrockmendel]

Based on tests it looks like this is not the correct next step. Closing.