BUG: Period resample with length=0 doesn't set freq
- [x] tests added / passed
- [x] passes `git diff upstream/master | flake8 --diff`
- [x] whatsnew entry

given freq is not applied if data is empty.

```
s = pd.Series(index=pd.PeriodIndex([], freq='D'))
s.resample('M').mean()
# Series([], Freq: D, dtype: float64)
```
#### Expected

```
s.resample('M').mean()
# Series([], Freq: M, dtype: float64)
```

related to any of: https://github.com/pydata/pandas/issues/12871 ?
 Related to #12868. It must change `freq` also.

CC: @MaximilianR 
 Thanks for spotting this @sinhrks. This was my change so mea culpa.

Had a quick look and there are a few odd things going on:

1) Resampling an empty Series with an empty `PeriodIndex` fails to convert freq for PeriodIndex-ed Series, but works fine for non-PeriodIndex-ed Series:

``` python

In [34]: pd.Series(range(4)).reindex(pd.PeriodIndex([],freq='M'))
Out[34]: Series([], Freq: M, dtype: int64)
# works

In [43]: pd.Series([], index=pd.PeriodIndex([], freq='D')).reindex(pd.PeriodIndex([], freq='M'))
Out[43]: Series([], Freq: D, dtype: float64)
# freq is still 'D' - doesn't work
```

...if this worked, the current resampler implementation would work as expected

2) `_get_new_index` is creating a `float64` index, where it should be `int64`:

``` python
In [6]: s = pd.Series(index=pd.PeriodIndex([], freq='D'))
In [9]: resampler=s.resample('M')
In [13]: resampler._get_new_index()
Out[13]: PeriodIndex([], dtype='float64', freq='M')
```

...not sure if this is having any real consequences though

Would be better to have these root issues solved rather than add a fix for the symptoms here, but a fix for the symptoms is better than nothing.
 ## [Current coverage](https://codecov.io/gh/pydata/pandas/pull/13067?src=pr) is **84.14%**

> Merging [#13067](https://codecov.io/gh/pydata/pandas/pull/13067?src=pr) into [master](https://codecov.io/gh/pydata/pandas/branch/master?src=pr) will increase coverage by **+<.01%**

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@@             master     #13067   diff @@
==========================================
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==========================================
+ Hits          42256      42264     +8   
+ Misses         7971       7966     -5   
  Partials          0          0          
```
1. File `pandas/_version.py` (not in diff) was modified. [more](https://codecov.io/gh/pydata/pandas/commit/df13ccc437322456eea8596741089f750caa4740/changes?src=pr#70616E6461732F5F76657273696F6E2E7079) 
   - Misses `-5` 
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> Powered by [Codecov](https://codecov.io?src=pr). Last updated by [87b0f4d...df13ccc](https://codecov.io/gh/pydata/pandas/compare/87b0f4dc1e91571cc4dd933b7cb181b99606ad20...df13ccc437322456eea8596741089f750caa4740)
 @MaximilianR I think `.reindex` should raise `IncompatibleFrequency` if `freq` are mismatched, even if its length is 0.

```
# on current master
s = pd.Series(index=pd.PeriodIndex(['1970-01', '1970-02', '1970-03'], freq='M'))
s.reindex(pd.PeriodIndex(['1970-01-01'], freq='D'))
# IncompatibleFrequency: Input has different freq=D from PeriodIndex(freq=M)
```
 > I think .reindex shuld raise IncompatibleFrequency if freq are mismatched, even if its length is 0.

Agreed
 I removed a bunch of the if/thens and generally cleared some stuff up, including solving the issues above. The thrust is to solve the root causes of why empty indexes need to be handled differently, rather than adding more special casing

@sinhrks do you want to use this PR for this, or do you want me to start another? Assuming you think it's an improvement

``` python
From f1e9a6eaa8608cc21a6ca52d5ce6888ced7f4181 Mon Sep 17 00:00:00 2001
From: Maximilian Roos 
Date: Tue, 3 May 2016 21:18:21 -0400
Subject: [PATCH] Lots of clearing up PeriodIndex resampling behaviour

---
 pandas/core/groupby.py                |  2 +-
 pandas/tseries/period.py              |  2 +-
 pandas/tseries/resample.py            | 18 ++++++------------
 pandas/tseries/tests/test_resample.py |  4 +++-
 4 files changed, 11 insertions(+), 15 deletions(-)

diff --git a/pandas/core/groupby.py b/pandas/core/groupby.py
index 7a47911..3d197ac 100644
--- a/pandas/core/groupby.py
+++ b/pandas/core/groupby.py
@@ -2669,7 +2669,7 @@ class SeriesGroupBy(GroupBy):
     def _wrap_applied_output(self, keys, values, not_indexed_same=False):
         if len(keys) == 0:
             # GH #6265
-            return Series([], name=self.name)
+            return Series([], name=self.name, index=Index(keys))

         def _get_index():
             if self.grouper.nkeys > 1:
diff --git a/pandas/tseries/period.py b/pandas/tseries/period.py
index 478b255..61e0e85 100644
--- a/pandas/tseries/period.py
+++ b/pandas/tseries/period.py
@@ -271,7 +271,7 @@ class PeriodIndex(DatelikeOps, DatetimeIndexOpsMixin, Int64Index):
     @classmethod
     def _simple_new(cls, values, name=None, freq=None, **kwargs):
         if not getattr(values, 'dtype', None):
-            values = np.array(values, copy=False)
+            values = np.array(values, copy=False, dtype='int64')
         if is_object_dtype(values):
             return PeriodIndex(values, name=name, freq=freq, **kwargs)

diff --git a/pandas/tseries/resample.py b/pandas/tseries/resample.py
index 167c6c1..2240ab6 100644
--- a/pandas/tseries/resample.py
+++ b/pandas/tseries/resample.py
@@ -789,19 +789,17 @@ class PeriodIndexResampler(DatetimeIndexResampler):
         ax = self.ax

         new_index = self._get_new_index()
-        if len(new_index) == 0:
-            result = self._selected_obj
-            if isinstance(self._selected_obj.index, PeriodIndex):
-                result = result.asfreq(self.freq, how=self.convention)
-            return self._wrap_result(result.reindex(new_index))

         # Start vs. end of period
         memb = ax.asfreq(self.freq, how=self.convention)

         if is_subperiod(ax.freq, self.freq):
             # Downsampling
-            rng = np.arange(memb.values[0], memb.values[-1] + 1)
-            bins = memb.searchsorted(rng, side='right')
+            if len(new_index) == 0:
+                bins = []
+            else:
+                rng = np.arange(memb.values[0], memb.values[-1] + 1)
+                bins = memb.searchsorted(rng, side='right')
             grouper = BinGrouper(bins, new_index)
             return self._groupby_and_aggregate(how, grouper=grouper)
         elif is_superperiod(ax.freq, self.freq):
@@ -811,8 +809,7 @@ class PeriodIndexResampler(DatetimeIndexResampler):

         raise ValueError('Frequency {axfreq} cannot be '
                          'resampled to {freq}'.format(
-                             axfreq=ax.freq,
-                             freq=self.freq))
+                             axfreq=ax.freq, freq=self.freq))

     def _upsample(self, method, limit=None):
         """
@@ -835,9 +832,6 @@ class PeriodIndexResampler(DatetimeIndexResampler):
         obj = self.obj
         new_index = self._get_new_index()

-        if len(new_index) == 0:
-            return self._wrap_result(self._selected_obj.reindex(new_index))
-
         # Start vs. end of period
         memb = ax.asfreq(self.freq, how=self.convention)

diff --git a/pandas/tseries/tests/test_resample.py b/pandas/tseries/tests/test_resample.py
index c796277..346c546 100644
--- a/pandas/tseries/tests/test_resample.py
+++ b/pandas/tseries/tests/test_resample.py
@@ -2053,9 +2053,11 @@ class TestPeriodIndex(Base, tm.TestCase):

             for method in resample_methods:
                 result = getattr(s.resample(freq), method)()
-                assert_series_equal(result, expected)
+                if method!='ohlc':  # returns df
+                    assert_series_equal(result, expected, check_dtype=False)
                 self.assertEqual(result.index.freq, freq)

+
     def test_resample_count(self):

         # GH12774
-- 
2.6.3
```
 If yours includes the same fix in a better way, please issue another PR. I'll close this.
 superseded by #13079 
