FIX: PeriodIndex json roundtrip (#47747)

* FIX: PeriodIndex json roundtrip

* update changelog

* Update doc/source/whatsnew/v1.5.0.rst

Co-authored-by: Matthew Roeschke <[email protected]>

* simplify change and add specialized tests

* pep8 change

Co-authored-by: Matthew Roeschke <[email protected]>

Author: jmg-duarte

doc/source/whatsnew/v1.5.0.rst

@@ -956,6 +956,7 @@ I/O
 - Bug in :func:`read_sas` that scrambled column names (:issue:`31243`)
 - Bug in :func:`read_sas` with RLE-compressed SAS7BDAT files that contain 0x00 control bytes (:issue:`47099`)
 - Bug in :func:`read_parquet` with ``use_nullable_dtypes=True`` where ``float64`` dtype was returned instead of nullable ``Float64`` dtype (:issue:`45694`)
+- Bug in :meth:`DataFrame.to_json` where ``PeriodDtype`` would not make the serialization roundtrip when read back with :meth:`read_json` (:issue:`44720`)
 
 Period
 ^^^^^^

pandas/io/json/_table_schema.py

@@ -197,6 +197,9 @@ def convert_json_field_to_pandas_type(field) -> str | CategoricalDtype:
     elif typ == "datetime":
         if field.get("tz"):
             return f"datetime64[ns, {field['tz']}]"
+        elif field.get("freq"):
+            # GH#47747 using datetime over period to minimize the change surface
+            return f"period[{field['freq']}]"
         else:
             return "datetime64[ns]"
     elif typ == "any":

pandas/tests/io/json/test_json_table_schema.py

@@ -708,6 +708,44 @@ def test_read_json_table_orient_raises(self, index_nm, vals, recwarn):
         with pytest.raises(NotImplementedError, match="can not yet read "):
             pd.read_json(out, orient="table")
 
+    @pytest.mark.parametrize(
+        "index_nm",
+        [None, "idx", pytest.param("index", marks=pytest.mark.xfail), "level_0"],
+    )
+    @pytest.mark.parametrize(
+        "vals",
+        [
+            {"ints": [1, 2, 3, 4]},
+            {"objects": ["a", "b", "c", "d"]},
+            {"objects": ["1", "2", "3", "4"]},
+            {"date_ranges": pd.date_range("2016-01-01", freq="d", periods=4)},
+            {"categoricals": pd.Series(pd.Categorical(["a", "b", "c", "c"]))},
+            {
+                "ordered_cats": pd.Series(
+                    pd.Categorical(["a", "b", "c", "c"], ordered=True)
+                )
+            },
+            {"floats": [1.0, 2.0, 3.0, 4.0]},
+            {"floats": [1.1, 2.2, 3.3, 4.4]},
+            {"bools": [True, False, False, True]},
+            {
+                "timezones": pd.date_range(
+                    "2016-01-01", freq="d", periods=4, tz="US/Central"
+                )  # added in # GH 35973
+            },
+        ],
+    )
+    def test_read_json_table_period_orient(self, index_nm, vals, recwarn):
+        df = DataFrame(
+            vals,
+            index=pd.Index(
+                (pd.Period(f"2022Q{q}") for q in range(1, 5)), name=index_nm
+            ),
+        )
+        out = df.to_json(orient="table")
+        result = pd.read_json(out, orient="table")
+        tm.assert_frame_equal(df, result)
+
     @pytest.mark.parametrize(
         "idx",
         [