diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 96090904b829f..4d2323b1910df 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -1301,7 +1301,9 @@ def __add__(self, other):
             # as is_integer returns True for these
             if not is_period_dtype(self.dtype):
                 raise integer_op_not_supported(self)
-            result = self._time_shift(other)
+            result = cast("PeriodArray", self)._addsub_int_array_or_scalar(
+                other * self.freq.n, operator.add
+            )
 
         # array-like others
         elif is_timedelta64_dtype(other_dtype):
@@ -1357,7 +1359,9 @@ def __sub__(self, other):
             # as is_integer returns True for these
             if not is_period_dtype(self.dtype):
                 raise integer_op_not_supported(self)
-            result = self._time_shift(-other)
+            result = cast("PeriodArray", self)._addsub_int_array_or_scalar(
+                other * self.freq.n, operator.sub
+            )
 
         elif isinstance(other, Period):
             result = self._sub_period(other)
diff --git a/pandas/core/arrays/period.py b/pandas/core/arrays/period.py
index fd5944fb63954..dd57bb9d121fd 100644
--- a/pandas/core/arrays/period.py
+++ b/pandas/core/arrays/period.py
@@ -549,10 +549,7 @@ def _time_shift(self, periods: int, freq=None) -> PeriodArray:
                 "`freq` argument is not supported for "
                 f"{type(self).__name__}._time_shift"
             )
-        values = self.asi8 + periods * self.freq.n
-        if self._hasna:
-            values[self._isnan] = iNaT
-        return type(self)(values, freq=self.freq)
+        return self + periods
 
     def _box_func(self, x) -> Period | NaTType:
         return Period._from_ordinal(ordinal=x, freq=self.freq)