[WIP]: API ExtensionDtype for DTA & TDA
Closes https://github.com/pandas-dev/pandas/issues/24662

TODO:

- [ ] Dedicated tests for new is_<foo> types
- [ ] Run the extension dtype tests for new dtypes
- [ ] (maybe?) see if the new EA tests pass for the new arrays. Tricky, since they aren't allowed internally. g
- [ ] failing dtype validation tests

This is going to fail. Going offline for a bit, but putting this up right now.

I'm going to clean up the changes in `internals` and the series constructor.
Still a WIP, but probably not going to have time to update this any further through the end of the week.
 > I would maybe instead just have a unified constructor that accepts tz=None for naive.

@jreback do you also mean just having a single class internally? `DatetimeDtype(tz=None)` is the naive one and `DatetimeDtype(tz=tz)` is the aware one (and `DatetimeTzDtype` can be kept as an alias for now for backwards compatibility) 

I didn't really think about any possible technical implications of that, but it seems logical to me to do that, since we also have a single DatetimeArray. Sorry I put this up in haste and didn't explain things well. Initially, I tried that, but ran into some difficulties. It turns out that having `pandas_dtype("M8[ns]")` return a non NumPy dtype breaks a lot of stuff. So I split them apart, and don't register the `DatetimeDtype`.

I'm not sure if it's possible to both

1. Have a DatetimeDtype that registers datetime64[ns, tz], but not datetime64[ns]
2. Have construct_from_string always work correctly

but I can try (later, not today). yeah I think this is a great idea @TomAugspurger but also possibly to involve changing some tricky code; would prefer to push this to 0.25 The main downside with pushing to 0.25 is it'll be an API breaking change for `DatetimeArray.dtype`, and `TimedeltaArray.dtype` with no path for deprecation.

---

just pushed an update, but still a WIP. # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24674?src=pr&el=h1) Report
> Merging [#24674](https://codecov.io/gh/pandas-dev/pandas/pull/24674?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/512830b46e678a1c6bd86cc60f54d74ff75792db?src=pr&el=desc) will **decrease** coverage by `0.02%`.
> The diff coverage is `88.23%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/24674/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/24674?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #24674      +/-   ##
==========================================
- Coverage   92.38%   92.36%   -0.03%     
==========================================
  Files         166      166              
  Lines       52379    52474      +95     
==========================================
+ Hits        48392    48467      +75     
- Misses       3987     4007      +20
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.78% <88.23%> (-0.03%)` | :arrow_down: |
| #single | `42.98% <72.94%> (+0.07%)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/24674?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/nanops.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvbmFub3BzLnB5) | `94.36% <ø> (ø)` | :arrow_up: |
| [pandas/core/api.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXBpLnB5) | `100% <ø> (ø)` | :arrow_up: |
| [pandas/core/series.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvc2VyaWVzLnB5) | `93.7% <100%> (+0.01%)` | :arrow_up: |
| [pandas/core/dtypes/common.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZHR5cGVzL2NvbW1vbi5weQ==) | `96.86% <100%> (+0.08%)` | :arrow_up: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `96.93% <100%> (ø)` | :arrow_up: |
| [pandas/core/arrays/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lcy5weQ==) | `97.78% <100%> (ø)` | :arrow_up: |
| [pandas/core/indexes/timedeltas.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy90aW1lZGVsdGFzLnB5) | `90.3% <100%> (+0.08%)` | :arrow_up: |
| [pandas/core/indexes/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZXMucHk=) | `96.28% <100%> (+0.01%)` | :arrow_up: |
| [pandas/core/indexes/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9iYXNlLnB5) | `96.3% <100%> (ø)` | :arrow_up: |
| [pandas/core/internals/construction.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW50ZXJuYWxzL2NvbnN0cnVjdGlvbi5weQ==) | `94% <60.86%> (-1.94%)` | :arrow_down: |
| ... and [10 more](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree-more) | |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24674?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24674?src=pr&el=footer). Last update [512830b...2abda43](https://codecov.io/gh/pandas-dev/pandas/pull/24674?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24674?src=pr&el=h1) Report
> Merging [#24674](https://codecov.io/gh/pandas-dev/pandas/pull/24674?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/0bd454cdc9307d3a7e73403c49cc8350965628ce?src=pr&el=desc) will **decrease** coverage by `49.41%`.
> The diff coverage is `73.65%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/24674/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/24674?src=pr&el=tree)

```diff
@@             Coverage Diff             @@
##           master   #24674       +/-   ##
===========================================
- Coverage   92.38%   42.97%   -49.42%     
===========================================
  Files         166      166               
  Lines       52366    52469      +103     
===========================================
- Hits        48380    22550    -25830     
- Misses       3986    29919    +25933
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `?` | |
| #single | `42.97% <73.65%> (+0.06%)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/24674?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/nanops.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvbmFub3BzLnB5) | `31.27% <ø> (-63.1%)` | :arrow_down: |
| [pandas/core/api.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXBpLnB5) | `86.66% <ø> (-13.34%)` | :arrow_down: |
| [pandas/core/series.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvc2VyaWVzLnB5) | `49.03% <100%> (-44.66%)` | :arrow_down: |
| [pandas/core/dtypes/common.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZHR5cGVzL2NvbW1vbi5weQ==) | `71.15% <100%> (-25.63%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `35.82% <100%> (-61.11%)` | :arrow_down: |
| [pandas/core/arrays/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lcy5weQ==) | `66.13% <100%> (-31.65%)` | :arrow_down: |
| [pandas/core/indexes/timedeltas.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy90aW1lZGVsdGFzLnB5) | `44.87% <100%> (-45.38%)` | :arrow_down: |
| [pandas/core/indexes/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZXMucHk=) | `48.62% <100%> (-47.65%)` | :arrow_down: |
| [pandas/core/indexes/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9iYXNlLnB5) | `56.49% <100%> (-39.82%)` | :arrow_down: |
| [pandas/core/internals/construction.py](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW50ZXJuYWxzL2NvbnN0cnVjdGlvbi5weQ==) | `62.11% <60.86%> (-33.83%)` | :arrow_down: |
| ... and [136 more](https://codecov.io/gh/pandas-dev/pandas/pull/24674/diff?src=pr&el=tree-more) | |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24674?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24674?src=pr&el=footer). Last update [0bd454c...f1ecb8b](https://codecov.io/gh/pandas-dev/pandas/pull/24674?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 Somewhat awkward API corner: what's the expected types for

1. `DatetimeArray.astype("M8[ns]")`
2. `DatetimeArray.astype(np.dtype("M8[ns]"))`
3. `DatetimeArray.astype(pd.DatetimeDtype())`

Previously, we'd use `.astype('M8[ns]')` to convert to an ndarray. But now that we have a dtype roughly equivalent to `M8[ns]`, should we keep doing that?

Another one, what should we do about `pd.DatetimeDtype() == "M8[ns]"` or `== np.dtpye("M8[ns]")`.

NumPy doesn't make this easy, since they would raise if the operands were flipped, rather than returning NotImplemented. For the expected types, I also have been wondering about this in general. So eg also for `DTA.astype("int64")`. 
Because we now have `PandasArray` and `PandasDtype`, so we could also return those? Similarly as `pd.array(DTA, dtype='int64')` does return that, we could do the same for `EA.astype`. It could be a specification of `EA.astype` that the return value is always another EA. Yeah, it's not obvious to me what's best here.

On the one hand, you could say that `.astype(np.dtype(.))` should always return an ndarray.

On the other hand, is it weird for `.astype(np.dtype("int64"))` to not match `.astype("int64")`? I suppose we'll need to sort all this out.

I'm really not sure what to do here :/ > @TomAugspurger: Yeah, it's not obvious to me what's best here.
On the one hand, you could say that `.astype(np.dtype(.))` should always return an ndarray.
On the other hand, is it weird for `.astype(np.dtype("int64"))` to not match `.astype("int64")`? I suppose we'll need to sort all this out.
I'm really not sure what to do here :/

How about `.astype` and `pd.array` always returning `PandasDType` (yes, even for an `np.dtype`)? If the user really wants an `ndarray`, they can then call `to_numpy`. That would in many ways be more consistent - and could later be extended to the point that the *only* way to get an `ndarray` from pandas is to call `to_numpy`. This has been inactive for a while.  Still a goal? I'm not sure. The API changes are tricky to get right.

Regardless, I don't think things will be done on this branch. I'll post an update on the issue.