REGR: Make comparisons consistent for PeriodDtype

doc/source/whatsnew/v1.1.4.rst

@@ -21,6 +21,7 @@ Fixed regressions
 - Fixed regression in :meth:`Series.astype` converting ``None`` to ``"nan"`` when casting to string (:issue:`36904`)
 - Fixed regression in :class:`RollingGroupby` causing a segmentation fault with Index of dtype object (:issue:`36727`)
 - Fixed regression in :meth:`DataFrame.resample(...).apply(...)` raised ``AttributeError`` when input was a :class:`DataFrame` and only a :class:`Series` was evaluated (:issue:`36951`)
+- Fixed regression in :class:`PeriodDtype` comparing both equal and unequal to its string representation (:issue:`37265`)
 
 .. ---------------------------------------------------------------------------
 

pandas/core/dtypes/dtypes.py

@@ -907,6 +907,9 @@ def __eq__(self, other: Any) -> bool:
 
         return isinstance(other, PeriodDtype) and self.freq == other.freq
 
+    def __ne__(self, other: Any) -> bool:
+        return not self.__eq__(other)
+
     def __setstate__(self, state):
         # for pickle compat. __getstate__ is defined in the
         # PandasExtensionDtype superclass and uses the public properties to

pandas/tests/dtypes/test_dtypes.py

@@ -991,3 +991,10 @@ def test_is_dtype_no_warning(check):
 
     with tm.assert_produces_warning(None):
         check(data["A"])
+
+
+def test_period_dtype_compare_to_string():
+    # https://github.com/pandas-dev/pandas/issues/37265
+    dtype = PeriodDtype(freq="M")
+    assert (dtype == "period[M]") is True
+    assert (dtype != "period[M]") is False