BUG: #57972 kurtosis small sample size low variance false positive cutoff

doc/source/whatsnew/v3.0.0.rst

@@ -324,6 +324,7 @@ Bug fixes
 - Fixed bug in :meth:`Series.diff` allowing non-integer values for the ``periods`` argument. (:issue:`56607`)
 - Fixed bug in :meth:`Series.rank` that doesn't preserve missing values for nullable integers when ``na_option='keep'``. (:issue:`56976`)
 - Fixed bug in :meth:`Series.replace` and :meth:`DataFrame.replace` inconsistently replacing matching instances when ``regex=True`` and missing values are present. (:issue:`56599`)
+- Fixed bug in :meth:`Series.rolling.kurt` with small sized values arrays with low variance getting zeroed out even when numerically stable (:issue:`57972`)
 
 Categorical
 ^^^^^^^^^^^

pandas/_libs/window/aggregations.pyx

@@ -712,7 +712,8 @@ cdef float64_t calc_kurt(int64_t minp, int64_t nobs,
             #         if the variance is less than 1e-14, it could be
             #         treat as zero, here we follow the original
             #         skew/kurt behaviour to check B <= 1e-14
-            if B <= 1e-14:
+            # #57972: for small arrays the cutoff can be lowered
+            if B <= 1e-14 and nobs > 100 or B <= 1e-16:
                 result = NaN
             else:
                 K = (dnobs * dnobs - 1.) * D / (B * B) - 3 * ((dnobs - 1.) ** 2)

pandas/core/nanops.py

@@ -1357,9 +1357,13 @@ def nankurt(
     # floating point error
     #
     # #18044 in _libs/windows.pyx calc_kurt follow this behavior
-    # to fix the fperr to treat denom <1e-14 as zero
-    numerator = _zero_out_fperr(numerator)
-    denominator = _zero_out_fperr(denominator)
+    # to fix the fperr to treat denom <1e-14 as zero (default cutoff)
+    # GH-57972 set cutoff lower for small arrays to prevent cutoff of otherwise
+    # numerically stable values
+    length = count[0] if isinstance(count, np.ndarray) else count
+    cutoff = 1e-14 if length > 100 else 1e-16
+    numerator = _zero_out_fperr(numerator, cutoff)
+    denominator = _zero_out_fperr(denominator, cutoff)
 
     if not isinstance(denominator, np.ndarray):
         # if ``denom`` is a scalar, check these corner cases first before
@@ -1576,12 +1580,12 @@ def check_below_min_count(
     return False
 
 
-def _zero_out_fperr(arg):
+def _zero_out_fperr(arg, cutoff=1e-14):
     # #18044 reference this behavior to fix rolling skew/kurt issue
     if isinstance(arg, np.ndarray):
-        return np.where(np.abs(arg) < 1e-14, 0, arg)
+        return np.where(np.abs(arg) < cutoff, 0, arg)
     else:
-        return arg.dtype.type(0) if np.abs(arg) < 1e-14 else arg
+        return arg.dtype.type(0) if np.abs(arg) < cutoff else arg
 
 
 @disallow("M8", "m8")

pandas/tests/test_nanops.py

@@ -1105,6 +1105,18 @@ def test_nans_skipna(self, samples, actual_kurt):
         kurt = nanops.nankurt(samples, skipna=True)
         tm.assert_almost_equal(kurt, actual_kurt)
 
+    def test_small_arrays_with_low_variance(self):
+        # GH-57972
+        # small sample arrays with low variance have a lower threshold for breakdown
+        # of numerical stability and should be handled accordingly
+        low_var_samples = np.array(
+            [-2.05191341e-05] + [0.0e00] * 4 + [-4.10391103e-05] + [0.0e00] * 23
+        )
+        # calculated with scipy.status kurtosis(low_var_samples, bias=False)
+        scipy_kurt = 18.087646853025614
+        kurt = nanops.nankurt(low_var_samples)
+        tm.assert_almost_equal(kurt, scipy_kurt)
+
     @property
     def prng(self):
         return np.random.default_rng(2)