It looks like a bug in older Pandas version. I could reproduce on an old installation Python 3.6.2 64 bit on win32, Pandas 1.0.3, numpy 1.15.4:
>>> s3.rolling(20,min_periods=3).kurt().tail(10)
890 9.591071
891 9.591071
892 9.591071
893 9.591071
894 19.663685
895 15.248361
896 40.444894
897 1368.233241
898 251407.375343
899 902540.031652
dtype: float64
It seems to be fixed on my newer version, Python 3.8.4 64 bit, Pandas 1.2.2, numpy 1.20.1:
>>> s3.rolling(20,min_periods=3).kurt().tail(10)
890 9.591067
891 9.591067
892 9.591067
893 9.591067
894 19.663666
895 14.872262
896 14.147158
897 16.716989
898 7.037037
899 20.000000
dtype: float64
both installations on the same Windows 10 machine.
I cannot say which component (Pandas or numpy) is the cause. As your tests using numpy.stats.kurtosis give correct result, I would suspect Pandas, but without further analysis by Pandas experts (and I am not one) I cannot be affirmative.
IMHO, the most reasonable solution is either to upgrade your system, or add a fresh new independant Python installation with the last possible Pandas version.
Answer from Serge Ballesta on Stack OverflowPandas
pandas.pydata.org › pandas-docs › stable › reference › api › pandas.core.window.rolling.Rolling.kurt.html
pandas.core.window.rolling.Rolling.kurt — pandas 2.3.3 documentation
The example below will show a rolling calculation with a window size of four matching the equivalent function call using scipy.stats. >>> arr = [1, 2, 3, 4, 999] >>> import scipy.stats >>> print(f"{scipy.stats.kurtosis(arr[:-1], bias=False):.6f}") -1.200000 >>> print(f"{scipy.stats.kurtosis(arr[1:], bias=False):.6f}") 3.999946 >>> s = pd.Series(arr) >>> s.rolling(4).kurt() 0 NaN 1 NaN 2 NaN 3 -1.200000 4 3.999946 dtype: float64
Runebook.dev
runebook.dev › en › docs › pandas › reference › api › pandas.core.window.rolling.rolling.kurt
The Pandas rolling().kurt() Method: A Practical Guide to Window Functions
The kurtosis calculation requires a minimum of 4 periods (observations) to be computed. If your window size is 4 or more, the first N−1 results will be NaN, where N is your window size.
Pandas
pandas.pydata.org › pandas-docs › version › 1.1 › reference › api › pandas.core.window.rolling.Rolling.kurt.html
pandas.core.window.rolling.Rolling.kurt — pandas 1.1.5 documentation
This function uses Fisher’s definition of kurtosis without bias. ... Under Review. ... Returned object type is determined by the caller of the rolling calculation.
Pandas
pandas.pydata.org › pandas-docs › version › 1.0.4 › reference › api › pandas.core.window.rolling.Rolling.kurt.html
pandas.core.window.rolling.Rolling.kurt — pandas 1.0.4 documentation
>>> arr = [1, 2, 3, 4, 999] >>> import scipy.stats >>> print(f"{scipy.stats.kurtosis(arr[:-1], bias=False):.6f}") -1.200000 >>> print(f"{scipy.stats.kurtosis(arr[1:], bias=False):.6f}") 3.999946 >>> s = pd.Series(arr) >>> s.rolling(4).kurt() 0 NaN 1 NaN 2 NaN 3 -1.200000 4 3.999946 dtype: float64 · pandas.core.window.rolling.Rolling.skew pandas.core.window.rolling.Rolling.apply
Pandas
pandas.pydata.org › docs › reference › api › pandas.DataFrame.kurtosis.html
pandas.DataFrame.kurtosis — pandas 3.0.6 documentation
Kurtosis obtained using Fisher’s definition of kurtosis (kurtosis of normal == 0.0).
Pandas
pandas.pydata.org › docs › dev › reference › api › pandas.core.window.rolling.Rolling.kurt.html
pandas.core.window.rolling.Rolling.kurt — pandas 3.0.0.dev0+2413.ge87248e1a5 documentation
Calculate the rolling Fisher’s definition of kurtosis without bias.
Pandas
pandas.pydata.org › pandas-docs › version › 1.3 › reference › api › pandas.core.window.rolling.Rolling.kurt.html
pandas.core.window.rolling.Rolling.kurt — pandas 1.3.5 documentation
Calculate the rolling Fisher’s definition of kurtosis without bias.
Pandas
pandas.pydata.org › pandas-docs › stable › generated › pandas.core.window.Rolling.kurt.html
Pydata
The page has been moved to this page
Pythontic
pythontic.com › pandas › dataframe-computations › kurtosis
kurtosis function in pandas | Pythontic.com
The pandas DataFrame has a computing method kurtosis() which computes the kurtosis for a set of values across a specific axis (i.e., a row or a column).
Pandas
pandas.pydata.org › docs › reference › api › pandas.core.window.rolling.Rolling.skew.html
pandas.core.window.rolling.Rolling.skew — pandas 2.3.3 documentation
Calculate the rolling unbiased skewness · Include only float, int, boolean columns
Pandas
pandas.pydata.org › pandas-docs › stable › reference › api › pandas.DataFrame.kurtosis.html
pandas.DataFrame.kurtosis — pandas 3.0.0 documentation
Kurtosis obtained using Fisher’s definition of kurtosis (kurtosis of normal == 0.0).
GitHub
github.com › pandas-dev › pandas › issues › 5749
Rolling skewness and kurtosis fail on a sample of all equal values · Issue #5749 · pandas-dev/pandas
December 19, 2013 - If one value occurs more times in a row than than the size of the window, the entire rolling computation fails, rather than just returning NaN for that one period (which is what I'd expect). For reference, scipy gives a kurtosis of -3 and a skewness of 0 (plus a warning) for this situation, which is not what I'd expect (since the higher moments are all zero, implying a division by zero).
Author: pandas-dev
GitHub
github.com › pandas-dev › pandas › issues › 18044
rolling skew and rolling kurt has wrong answer under all eq values · Issue #18044 · pandas-dev/pandas
October 31, 2017 - Code Sample, a copy-pastable example if possible pd.Series([1.1]*15).rolling(10).skew() pd.Series([1.1]*15).rolling(10).kurt() Problem description rolling skew() wrong result: pd.Series([1.1]*15).rolling(10).skew() 0 NaN 1 NaN 2 NaN 3 Na...
Author: pandas-dev
GitHub
github.com › ajcr › rolling › issues › 2
Implement rolling skew and rolling kurtosis methods · Issue #2 · ajcr/rolling
December 31, 2017 - pandas has implementations for rolling skew and rolling kurtosis. The implementations can be seen here.
Author: ajcr
Trading Strategy
tradingstrategy.ai › docs › api › technical-analysis › statistics › help › pandas_ta.statistics.kurtosis.html
kurtosis function in pandas_ta.statistics
API documentation for pandas_ta.statistics.kurtosis Python function. kurtosis(close, length=None, offset=None, **kwargs)[source]# Rolling Kurtosis · Sources: Calculation: Default Inputs: length=30 · KURTOSIS = close.rolling(length).kurt() Args: close (pd.Series): Series of ‘close’s length (int): It’s period.
GitHub
github.com › pandas-dev › pandas › issues › 58711
BUG: numerical inconsistency in calculating rolling kurtosis · Issue #58711 · pandas-dev/pandas
May 14, 2024 - import pandas as pd series_1 = pd.Series([-1] + ([1] * 19)) print(series_1.kurt()) print(series_1.rolling(20).kurt().max()) series_2 = pd.Series(([-1] * 7) + ([1] * 19)) print(series_2.rolling(20).kurt().max()) series_3 = pd.Series(([-1] * 6) + ([1] * 19)) print(series_3.rolling(20).kurt().max()) I met a problem in calculating rolling kurtosis for a specific kind of data.
Author: pandas-dev
Medium
medium.com › @atanudan › kurtosis-skew-function-in-pandas-aa63d72e20de
Kurtosis() & Skew() Function In Pandas | by Atanu Dan | Medium
September 16, 2020 - Skewness essentially measures the symmetry of the distribution, while kurtosis determines the heaviness of the distribution tails.
Top answer 1 of 2
3
The pandas documentation says the following
Return unbiased kurtosis over requested axis using Fisher’s definition of kurtosis (kurtosis of normal == 0.0)
This is probably the excess kurtosis, defined as kurtosis - 3.
2 of 2
3
Pandas is calculating the UNBIASED estimator of the excess Kurtosis. Kurtosis is the normalized 4th central moment. To find the unbiased estimators of the cumulants you need the k-statistics.
So the unbiased estimator of kurtosis is (k4/k2**2)
To illustrate this:
import pandas as pd
import numpy as np
np.random.seed(11234)
test_series = pd.Series(np.random.randn(5000))
test_series.kurtosis()
#-0.0411811269445872
Now we can calculate this explicitly using the k-statistics:
n = len(test_series)
S1 = test_series.pow(1).sum()
S2 = test_series.pow(2).sum()
S3 = test_series.pow(3).sum()
S4 = test_series.pow(4).sum()
# Eq (7) and (5) from the k-statistics link
k4 = (-6*S1**4 + 12*n*S1**2*S2 - 3*n*(n-1)*S2**2 -4*n*(n+1)*S1*S3 + n**2*(n+1)*S4)/(n*(n-1)*(n-2)*(n-3))
k2 = (n*S2-S1**2)/(n*(n-1))
# k2 is the same as the N-1 variance: test_series.std(ddof=1)**2
k4/k2**2
#-0.04118112694458816
If you want better agreement to more decimal places, you'll need to be careful with the sums as they get rather large. But they're identical to 12 places.