BUG: Aligned skew and kurt results with scipy.stats

doc/source/whatsnew/v2.3.3.rst

@@ -53,6 +53,10 @@ Bug fixes
   characters as digits for :class:`StringDtype` backed by PyArrow (:issue:`61466`)
 - Fix comparing a :class:`StringDtype` Series with mixed objects raising an error (:issue:`60228`)
 - Fix error being raised when using a numpy ufunc with a Python-backed string array (:issue:`40800`)
+- Fix bug in :meth:`Series.rolling` and :meth:`DataFrame.rolling` ``skew()`` and ``kurt()`` calculations
+  that produced incorrect values for windows containing variance of zero.
+  The implementation has been updated to return ``NaN`` in these cases, matching skipy.stats behavior
+  and the non-rolling :meth:`Series.skew` and :meth:`Series.kurt` received the same behavior ensuring consistency. (:issue:`62864`)
 
 Other changes
 ~~~~~~~~~~~~~

pandas/_libs/window/aggregations.pyx

@@ -498,10 +498,10 @@ cdef float64_t calc_skew(int64_t minp, int64_t nobs,
         if nobs < 3:
             result = NaN
         # GH 42064 46431
-        # uniform case, force result to be 0
+        # degenerate case, force result to be NaN
         elif num_consecutive_same_value >= nobs:
-            result = 0.0
-        # #18044: with uniform distribution, floating issue will
+            result = NaN
+        # #18044: with degenerate distribution, floating issue will
         #         cause B != 0. and cause the result is a very
         #         large number.
         #
@@ -694,7 +694,7 @@ cdef float64_t calc_kurt(int64_t minp, int64_t nobs,
         # GH 42064 46431
         # uniform case, force result to be -3.
         elif num_consecutive_same_value >= nobs:
-            result = -3.
+            result = NaN
         else:
             dnobs = <float64_t>nobs
             A = x / dnobs

pandas/core/nanops.py

@@ -1287,10 +1287,10 @@ def nanskew(
         result = result.astype(dtype, copy=False)
 
     if isinstance(result, np.ndarray):
-        result = np.where(m2 == 0, 0, result)
+        result = np.where(m2 == 0, np.nan, result)
         result[count < 3] = np.nan
     else:
-        result = dtype.type(0) if m2 == 0 else result
+        result = np.nan if m2 == 0 else result
         if count < 3:
             return np.nan
 
@@ -1400,7 +1400,7 @@ def nankurt(
         if count < 4:
             return np.nan
         if denominator == 0:
-            return values.dtype.type(0)
+            return np.nan
 
     with np.errstate(invalid="ignore", divide="ignore"):
         result = numerator / denominator - adj
@@ -1410,7 +1410,7 @@ def nankurt(
         result = result.astype(dtype, copy=False)
 
     if isinstance(result, np.ndarray):
-        result = np.where(denominator == 0, 0, result)
+        result = np.where(denominator == 0, np.nan, result)
         result[count < 4] = np.nan
 
     return result

pandas/tests/reductions/test_stat_reductions.py

@@ -9,7 +9,6 @@
 
 import pandas as pd
 from pandas import (
-    DataFrame,
     Series,
     date_range,
 )
@@ -228,47 +227,10 @@ def test_sem(self):
         result = s.sem(ddof=1)
         assert pd.isna(result)
 
-    def test_skew(self):
-        sp_stats = pytest.importorskip("scipy.stats")
-
-        string_series = Series(range(20), dtype=np.float64, name="series")
-
-        alt = lambda x: sp_stats.skew(x, bias=False)
-        self._check_stat_op("skew", alt, string_series)
-
-        # test corner cases, skew() returns NaN unless there's at least 3
-        # values
-        min_N = 3
-        for i in range(1, min_N + 1):
-            s = Series(np.ones(i))
-            df = DataFrame(np.ones((i, i)))
-            if i < min_N:
-                assert np.isnan(s.skew())
-                assert np.isnan(df.skew()).all()
-            else:
-                assert 0 == s.skew()
-                assert isinstance(s.skew(), np.float64)  # GH53482
-                assert (df.skew() == 0).all()
-
     def test_kurt(self):
         sp_stats = pytest.importorskip("scipy.stats")
 
         string_series = Series(range(20), dtype=np.float64, name="series")
 
         alt = lambda x: sp_stats.kurtosis(x, bias=False)
         self._check_stat_op("kurt", alt, string_series)
-
-    def test_kurt_corner(self):
-        # test corner cases, kurt() returns NaN unless there's at least 4
-        # values
-        min_N = 4
-        for i in range(1, min_N + 1):
-            s = Series(np.ones(i))
-            df = DataFrame(np.ones((i, i)))
-            if i < min_N:
-                assert np.isnan(s.kurt())
-                assert np.isnan(df.kurt()).all()
-            else:
-                assert 0 == s.kurt()
-                assert isinstance(s.kurt(), np.float64)  # GH53482
-                assert (df.kurt() == 0).all()

pandas/tests/test_nanops.py

@@ -559,10 +559,10 @@ def _skew_kurt_wrap(self, values, axis=None, func=None):
         result = func(values, axis=axis, bias=False)
         # fix for handling cases where all elements in an axis are the same
         if isinstance(result, np.ndarray):
-            result[np.max(values, axis=axis) == np.min(values, axis=axis)] = 0
+            result[np.max(values, axis=axis) == np.min(values, axis=axis)] = np.nan
             return result
         elif np.max(values) == np.min(values):
-            return 0.0
+            return np.nan
         return result
 
     def test_nanskew(self, skipna):
@@ -1021,7 +1021,7 @@ def test_constant_series(self, val):
         # xref GH 11974
         data = val * np.ones(300)
         skew = nanops.nanskew(data)
-        assert skew == 0.0
+        assert np.isnan(skew)
 
     def test_all_finite(self):
         alpha, beta = 0.3, 0.1
@@ -1089,7 +1089,7 @@ def test_constant_series(self, val):
         # xref GH 11974
         data = val * np.ones(300)
         kurt = nanops.nankurt(data)
-        tm.assert_equal(kurt, 0.0)
+        tm.assert_equal(kurt, np.nan)
 
     def test_all_finite(self):
         alpha, beta = 0.3, 0.1

pandas/tests/window/test_rolling.py

@@ -1833,10 +1833,12 @@ def test_rolling_skew_kurt_floating_artifacts():
 
     sr = Series([1 / 3, 4, 0, 0, 0, 0, 0])
     r = sr.rolling(4)
+
     result = r.skew()
-    assert (result[-2:] == 0).all()
+    assert np.isnan(result[-2:]).all()
+
     result = r.kurt()
-    assert (result[-2:] == -3).all()
+    assert np.isnan(result[-2:]).all()
 
 
 def test_numeric_only_frame(arithmetic_win_operators, numeric_only):

pandas/tests/window/test_rolling_skew_kurt.py

@@ -170,7 +170,7 @@ def test_center_reindex_frame(frame, roll_func):
 
 
 def test_rolling_skew_edge_cases(step):
-    expected = Series([np.nan] * 4 + [0.0])[::step]
+    expected = Series([np.nan] * 5)[::step]
     # yields all NaN (0 variance)
     d = Series([1] * 5)
     x = d.rolling(window=5, step=step).skew()
@@ -191,7 +191,7 @@ def test_rolling_skew_edge_cases(step):
 
 
 def test_rolling_kurt_edge_cases(step):
-    expected = Series([np.nan] * 4 + [-3.0])[::step]
+    expected = Series([np.nan] * 5)[::step]
 
     # yields all NaN (0 variance)
     d = Series([1] * 5)
@@ -212,16 +212,12 @@ def test_rolling_kurt_edge_cases(step):
 
 
 def test_rolling_skew_eq_value_fperr(step):
-    # #18804 all rolling skew for all equal values should return Nan
-    # #46717 update: all equal values should return 0 instead of NaN
+    # #18804 all rolling skew for all equal values should return NaN
     a = Series([1.1] * 15).rolling(window=10, step=step).skew()
-    assert (a[a.index >= 9] == 0).all()
-    assert a[a.index < 9].isna().all()
+    assert a.isna().all()
 
 
 def test_rolling_kurt_eq_value_fperr(step):
     # #18804 all rolling kurt for all equal values should return Nan
-    # #46717 update: all equal values should return -3 instead of NaN
     a = Series([1.1] * 15).rolling(window=10, step=step).kurt()
-    assert (a[a.index >= 9] == -3).all()
-    assert a[a.index < 9].isna().all()
+    assert a.isna().all()