PERF: Poor numerical stability of rolling_kurt and rolling_skew

[jaimefrio]

The numerical stability of the current implementation of rolling_kurt and rolling_skew is very poor:

In [14]: x = np.random.rand(10)

In [15]: pd.Series(x).rolling(4).skew()
Out[15]:
0         NaN
1         NaN
2         NaN
3   -0.971467
4    0.596391
5   -1.163135
6   -0.611469
7   -1.624713
8   -0.021832
9    0.754653
dtype: float64

In [16]: pd.Series(x + 5000).rolling(4).skew()
Out[16]:
0         NaN
1         NaN
2         NaN
3   -0.968964
4    0.608522
5   -1.171751
6   -0.619354
7   -1.628942
8   -0.033949
9    0.741304
dtype: float64

In [17]: pd.Series(x).rolling(4).kurt()
Out[17]:
0         NaN
1         NaN
2         NaN
3    2.030185
4   -2.647975
5    1.183004
6   -2.178587
7    2.658058
8   -4.258505
9    0.939264
dtype: float64

In [18]: pd.Series(x + 100).rolling(4).kurt()
Out[18]:
0         NaN
1         NaN
2         NaN
3    2.030230
4   -2.648801
5    1.182382
6   -2.178574
7    2.657934
8   -4.258813
9    0.938661
dtype: float64

This can be solved using an updating algorithm, similar to what is done in #6817 for rolling_var.

[dsm054]

I think this can be closed. It was fixed in #6817, and #7297 is open to address the secondary issues that introduced.

[jaimefrio]

#6817 fixed it for rolling_var (and just added #7572 that should fix #7297), but rolling_kurt and rolling_skew were unchanged by #6817, and have an even worse numerical stability than rolling_var. @jreback specifically asked me to open this issue as a placeholder, I am hoping to find some time during this summer to figure out the math and get those fixed as well.

[seth-p]

Note also #8086.