Hey OP, thanks for raising this! Rolling operations include not just the current row, but also previous rows within the window. This means including or excluding the first row can impact the entire calculation, even for later rows. This is expected behavior, not a bug.

Let me know if this makes sense or if you’re seeing something different.

@arthurlw Thank you for your reply! Regarding the function of df.rolling, I believe it builds a sliding window on the data and applies a calculation function. Each calculation only uses the data within the window. If following this logic, in the case I provided, when calculating the kurtosis, the following results will be my expectation:

res1 = df.rolling(20,min_periods=1).kurt()
res2 = df.iloc[1:].rolling(20,min_periods=1).kurt()

pd.testing.assert_frame_equal(res1.loc[21:], res2.loc[21:])

However, from the case I presented, it can be seen that the results are not like this. In my case, I constructed a special dataframe, which has a maximum value and a minimum value. The maximum value is located at index 0. Whether to include this value in the rolling calculation will lead to different results.

This is my understanding of df.rolling. Finally, once again, thank you for your reply.

Thanks for the explanation! You’re right that whether the first data point (index 0) is included will lead to different results. This is actually expected behavior because df.iloc[1:] explicitly removes the first row, which means all window calculations in res2 will start at index 1 and will exclude the value at index 0. Thus, res1 and res2 will provide different results.

Thank you for your reply. What surprises me is that the sliding window calculation shouldn't be affected by data outside the window. Then, including or excluding the first piece of data not affect the calculation result at the last index position. Since the data window is 20 and there are 100 data samples, why excluding the first data entry would cause the calculation result at the last index position to be different? This is the point that raises my doubts.

I see now what you mean and thanks for the catch! This definitely shouldn’t happen. It looks like the huge outlier is influencing values outside of its window with .std, .skew, and .kurt. PRs and contributions are welcome.

take

Rolling algos in pandas uses online methods, see: #60053 (comment)

Just an update, it seems like the current implementation is running into difficulty due to the value contrast between numbers being too large. There is a compensation number which works as a fallback to catch the changes in the small numbers, but because the data set here includes two equally large magnitudes (1e6, -1e6), the algorithm overwrites the compensation number which is what causes a knock-on effect for the running summation of x^4.