BUG: numerical inconsistency in calculating rolling kurtosis about pandas

[auderson]

The rolling algos in pandas generally use the online updating version for performance. It is expected the result can be a bit different due to floating point artifacts.
If you really want consistent result you can try rolling.apply(lambda x: x.kurt()), but this is much slower.

[HaloCollider]

The rolling algos in pandas generally use the online updating version for performance. It is expected the result can be a bit different due to floating point artifacts. If you really want consistent result you can try rolling.apply(lambda x: x.kurt()), but this is much slower.

I understand that the online updating method may cause numerical instability in a time-series manner. But 20.0 or larger than 20.0 is an overall characteristic of a series. In other words, you cannot get a 20.0 and a larger than 20.0 in a single series.

For example:
pd.Series([1] * 19 + [-1] * 7 + [1] * 1).rolling(20).kurt().max() gives a 20.00000000000001,
while
pd.Series([1] * 19 + [-1] * 7 + [1] * 2).rolling(20).kurt().max() gives a 20.0.
Their difference is just an additional 1 at the tail, which doesn't affect the max kurtosis from the view of online updating.

(That's also why I'm calling it inconsistency rather than instability.)

[auderson]

Looks like it's due to a demean operation prior to calculation:

pandas/pandas/_libs/window/aggregations.pyx

Lines 828 to 838 in 283a2dc

	for i in range(0, V):
	val = values_copy[i]
	if val == val:
	nobs_mean += 1
	sum_val += val
	mean_val = sum_val / nobs_mean
	# Other cases would lead to imprecision for smallest values
	if min_val - mean_val > -1e4:
	mean_val = round(mean_val)
	for i in range(0, V):
	values_copy[i] = values_copy[i] - mean_val

[HaloCollider]

Looks like it's due to a demean operation prior to calculation:

pandas/pandas/_libs/window/aggregations.pyx

Lines 828 to 838 in 283a2dc

	for i in range(0, V):
	val = values_copy[i]
	if val == val:
	nobs_mean += 1
	sum_val += val
	mean_val = sum_val / nobs_mean
	# Other cases would lead to imprecision for smallest values
	if min_val - mean_val > -1e4:
	mean_val = round(mean_val)
	for i in range(0, V):
	values_copy[i] = values_copy[i] - mean_val

Thanks a lot. This solves my issue. Previously I checked the source but missed the demean operation, which made my version produce consistent results that caused confusion.

I found the exact thresholds of the proportion of 1 of a series being 0.25 and 0.75, i.e., the mean being -0.5 and 0.5. Out of range (0.25 to 0.75) distributions lead to 20.0.