BUG: Index.__new__ with Interval/Period data and object dtype

pandas/core/indexes/base.py

@@ -291,11 +291,15 @@ def __new__(
             return CategoricalIndex(data, dtype=dtype, copy=copy, name=name, **kwargs)
 
         # interval
-        elif (
-            is_interval_dtype(data) or is_interval_dtype(dtype)
-        ) and not is_object_dtype(dtype):
-            closed = kwargs.get("closed", None)
-            return IntervalIndex(data, dtype=dtype, name=name, copy=copy, closed=closed)
+        elif is_interval_dtype(data) or is_interval_dtype(dtype):
+            closed = kwargs.pop("closed", None)
+            if is_dtype_equal(_o_dtype, dtype):
+                return IntervalIndex(
+                    data, name=name, copy=copy, closed=closed, **kwargs
+                ).astype(object)
+            return IntervalIndex(
+                data, dtype=dtype, name=name, copy=copy, closed=closed, **kwargs
+            )
 
         elif (
             is_datetime64_any_dtype(data)
@@ -325,8 +329,10 @@ def __new__(
             else:
                 return TimedeltaIndex(data, copy=copy, name=name, dtype=dtype, **kwargs)
 
-        elif is_period_dtype(data) and not is_object_dtype(dtype):
-            return PeriodIndex(data, copy=copy, name=name, **kwargs)
+        elif is_period_dtype(data) or is_period_dtype(dtype):
+            if is_dtype_equal(_o_dtype, dtype):
+                return PeriodIndex(data, copy=False, name=name, **kwargs).astype(object)
+            return PeriodIndex(data, dtype=dtype, copy=copy, name=name, **kwargs)
 
         # extension dtype
         elif is_extension_array_dtype(data) or is_extension_array_dtype(dtype):

pandas/tests/indexes/period/test_constructors.py

@@ -7,14 +7,11 @@
 
 import pandas as pd
 from pandas import Index, Period, PeriodIndex, Series, date_range, offsets, period_range
-import pandas.core.indexes.period as period
+from pandas.core.arrays import PeriodArray
 import pandas.util.testing as tm
 
 
 class TestPeriodIndex:
-    def setup_method(self, method):
-        pass
-
     def test_construction_base_constructor(self):
         # GH 13664
         arr = [pd.Period("2011-01", freq="M"), pd.NaT, pd.Period("2011-03", freq="M")]
@@ -32,6 +29,30 @@ def test_construction_base_constructor(self):
             pd.Index(np.array(arr)), pd.Index(np.array(arr), dtype=object)
         )
 
+    def test_base_constructor_with_period_dtype(self):
+        dtype = PeriodDtype("D")
+        values = ["2011-01-01", "2012-03-04", "2014-05-01"]
+        result = pd.Index(values, dtype=dtype)
+
+        expected = pd.PeriodIndex(values, dtype=dtype)
+        tm.assert_index_equal(result, expected)
+
+    @pytest.mark.parametrize(
+        "values_constructor", [list, np.array, PeriodIndex, PeriodArray._from_sequence]
+    )
+    def test_index_object_dtype(self, values_constructor):
+        # Index(periods, dtype=object) is an Index (not an PeriodIndex)
+        periods = [
+            pd.Period("2011-01", freq="M"),
+            pd.NaT,
+            pd.Period("2011-03", freq="M"),
+        ]
+        values = values_constructor(periods)
+        result = Index(values, dtype=object)
+
+        assert type(result) is Index
+        tm.assert_numpy_array_equal(result.values, np.array(values))
+
     def test_constructor_use_start_freq(self):
         # GH #1118
         p = Period("4/2/2012", freq="B")
@@ -201,7 +222,7 @@ def test_constructor_dtype(self):
         assert res.dtype == "period[M]"
 
         msg = "specified freq and dtype are different"
-        with pytest.raises(period.IncompatibleFrequency, match=msg):
+        with pytest.raises(IncompatibleFrequency, match=msg):
             PeriodIndex(["2011-01"], freq="M", dtype="period[D]")
 
     def test_constructor_empty(self):
@@ -261,25 +282,25 @@ def test_constructor_pi_nat(self):
     def test_constructor_incompat_freq(self):
         msg = "Input has different freq=D from PeriodIndex\\(freq=M\\)"
 
-        with pytest.raises(period.IncompatibleFrequency, match=msg):
+        with pytest.raises(IncompatibleFrequency, match=msg):
             PeriodIndex(
                 [Period("2011-01", freq="M"), pd.NaT, Period("2011-01", freq="D")]
             )
 
-        with pytest.raises(period.IncompatibleFrequency, match=msg):
+        with pytest.raises(IncompatibleFrequency, match=msg):
             PeriodIndex(
                 np.array(
                     [Period("2011-01", freq="M"), pd.NaT, Period("2011-01", freq="D")]
                 )
             )
 
         # first element is pd.NaT
-        with pytest.raises(period.IncompatibleFrequency, match=msg):
+        with pytest.raises(IncompatibleFrequency, match=msg):
             PeriodIndex(
                 [pd.NaT, Period("2011-01", freq="M"), Period("2011-01", freq="D")]
             )
 
-        with pytest.raises(period.IncompatibleFrequency, match=msg):
+        with pytest.raises(IncompatibleFrequency, match=msg):
             PeriodIndex(
                 np.array(
                     [pd.NaT, Period("2011-01", freq="M"), Period("2011-01", freq="D")]