diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index 0f07a9cf3c0e0..ac90483513af5 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -820,6 +820,25 @@ def to_period(self, freq=None):
 
         return PeriodArrayMixin(self.values, freq=freq)
 
+    def to_perioddelta(self, freq):
+        """
+        Calculate TimedeltaArray of difference between index
+        values and index converted to PeriodArray at specified
+        freq. Used for vectorized offsets
+
+        Parameters
+        ----------
+        freq: Period frequency
+
+        Returns
+        -------
+        TimedeltaArray/Index
+        """
+        # TODO: consider privatizing (discussion in GH#23113)
+        from pandas.core.arrays.timedeltas import TimedeltaArrayMixin
+        i8delta = self.asi8 - self.to_period(freq).to_timestamp().asi8
+        return TimedeltaArrayMixin(i8delta)
+
     # -----------------------------------------------------------------
     # Properties - Vectorized Timestamp Properties/Methods
 
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index e0219acc115b5..7fb7e24cce94e 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -42,7 +42,6 @@
 from pandas.tseries.offsets import (
     CDay, prefix_mapping)
 
-from pandas.core.tools.timedeltas import to_timedelta
 from pandas.util._decorators import Appender, cache_readonly, Substitution
 import pandas.core.common as com
 import pandas.tseries.offsets as offsets
@@ -545,13 +544,6 @@ def to_series(self, keep_tz=False, index=None, name=None):
 
         return Series(values, index=index, name=name)
 
-    @Appender(DatetimeArrayMixin.to_period.__doc__)
-    def to_period(self, freq=None):
-        from pandas.core.indexes.period import PeriodIndex
-
-        result = DatetimeArrayMixin.to_period(self, freq=freq)
-        return PeriodIndex(result, name=self.name)
-
     def snap(self, freq='S'):
         """
         Snap time stamps to nearest occurring frequency
@@ -623,23 +615,6 @@ def union(self, other):
                     result.freq = to_offset(result.inferred_freq)
             return result
 
-    def to_perioddelta(self, freq):
-        """
-        Calculate TimedeltaIndex of difference between index
-        values and index converted to periodIndex at specified
-        freq. Used for vectorized offsets
-
-        Parameters
-        ----------
-        freq: Period frequency
-
-        Returns
-        -------
-        y: TimedeltaIndex
-        """
-        return to_timedelta(self.asi8 - self.to_period(freq)
-                            .to_timestamp().asi8)
-
     def union_many(self, others):
         """
         A bit of a hack to accelerate unioning a collection of indexes
@@ -1168,6 +1143,9 @@ def slice_indexer(self, start=None, end=None, step=None, kind=None):
     is_year_end = wrap_field_accessor(DatetimeArrayMixin.is_year_end)
     is_leap_year = wrap_field_accessor(DatetimeArrayMixin.is_leap_year)
 
+    to_perioddelta = wrap_array_method(DatetimeArrayMixin.to_perioddelta,
+                                       False)
+    to_period = wrap_array_method(DatetimeArrayMixin.to_period, True)
     normalize = wrap_array_method(DatetimeArrayMixin.normalize, True)
     to_julian_date = wrap_array_method(DatetimeArrayMixin.to_julian_date,
                                        False)
diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index cbcd39317e17e..6c68ba2c35919 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -289,9 +289,9 @@ def __array_wrap__(self, result, context=None):
         """
         if isinstance(context, tuple) and len(context) > 0:
             func = context[0]
-            if (func is np.add):
+            if func is np.add:
                 pass
-            elif (func is np.subtract):
+            elif func is np.subtract:
                 name = self.name
                 left = context[1][0]
                 right = context[1][1]
@@ -312,7 +312,7 @@ def __array_wrap__(self, result, context=None):
             return result
         # the result is object dtype array of Period
         # cannot pass _simple_new as it is
-        return self._shallow_copy(result, freq=self.freq, name=self.name)
+        return type(self)(result, freq=self.freq, name=self.name)
 
     @property
     def size(self):
diff --git a/pandas/tests/arrays/test_datetimelike.py b/pandas/tests/arrays/test_datetimelike.py
index bfce5fb1462d9..ac7692c4afa74 100644
--- a/pandas/tests/arrays/test_datetimelike.py
+++ b/pandas/tests/arrays/test_datetimelike.py
@@ -67,6 +67,20 @@ def test_astype_object(self, tz_naive_fixture):
         assert asobj.dtype == 'O'
         assert list(asobj) == list(dti)
 
+    @pytest.mark.parametrize('freqstr', ['D', 'B', 'W', 'M', 'Q', 'Y'])
+    def test_to_perioddelta(self, datetime_index, freqstr):
+        # GH#23113
+        dti = datetime_index
+        arr = DatetimeArrayMixin(dti)
+
+        expected = dti.to_perioddelta(freq=freqstr)
+        result = arr.to_perioddelta(freq=freqstr)
+        assert isinstance(result, TimedeltaArrayMixin)
+
+        # placeholder until these become actual EA subclasses and we can use
+        #  an EA-specific tm.assert_ function
+        tm.assert_index_equal(pd.Index(result), pd.Index(expected))
+
     @pytest.mark.parametrize('freqstr', ['D', 'B', 'W', 'M', 'Q', 'Y'])
     def test_to_period(self, datetime_index, freqstr):
         dti = datetime_index