Computational tools
Statistical functions
Percent change
Series and DataFrame have a method pct_change() to compute the percent change over a given number of periods (using fill_method to fill NA/null values before computing the percent change).
In [1]: ser = pd.Series(np.random.randn(8))
In [2]: ser.pct_change()
Out[2]:
0 NaN
1 -1.602976
2 4.334938
3 -0.247456
4 -2.067345
5 -1.142903
6 -1.688214
7 -9.759729
dtype: float64
In [3]: df = pd.DataFrame(np.random.randn(10, 4))
In [4]: df.pct_change(periods=3)
Out[4]:
0 1 2 3
0 NaN NaN NaN NaN
1 NaN NaN NaN NaN
2 NaN NaN NaN NaN
3 -0.218320 -1.054001 1.987147 -0.510183
4 -0.439121 -1.816454 0.649715 -4.822809
5 -0.127833 -3.042065 -5.866604 -1.776977
6 -2.596833 -1.959538 -2.111697 -3.798900
7 -0.117826 -2.169058 0.036094 -0.067696
8 2.492606 -1.357320 -1.205802 -1.558697
9 -1.012977 2.324558 -1.003744 -0.371806
Covariance
Series.cov() can be used to compute covariance between series (excluding missing values).
In [5]: s1 = pd.Series(np.random.randn(1000))
In [6]: s2 = pd.Series(np.random.randn(1000))
In [7]: s1.cov(s2)
Out[7]: 0.000680108817431082
Analogously, DataFrame.cov() to compute pairwise covariances among the series in the DataFrame, also excluding NA/null values.
Note
Assuming the missing data are missing at random this results in an estimate for the covariance matrix which is unbiased. However, for many applications this estimate may not be acceptable because the estimated covariance matrix is not guaranteed to be positive semi-definite. This could lead to estimated correlations having absolute values which are greater than one, and/or a non-invertible covariance matrix. See Estimation of covariance matrices for more details.
In [8]: frame = pd.DataFrame(np.random.randn(1000, 5),
...: columns=['a', 'b', 'c', 'd', 'e'])
...:
In [9]: frame.cov()
Out[9]:
a b c d e
a 1.000882 -0.003177 -0.002698 -0.006889 0.031912
b -0.003177 1.024721 0.000191 0.009212 0.000857
c -0.002698 0.000191 0.950735 -0.031743 -0.005087
d -0.006889 0.009212 -0.031743 1.002983 -0.047952
e 0.031912 0.000857 -0.005087 -0.047952 1.042487
DataFrame.cov also supports an optional min_periods keyword that specifies the required minimum number of observations for each column pair in order to have a valid result.
In [10]: frame = pd.DataFrame(np.random.randn(20, 3), columns=['a', 'b', 'c'])
In [11]: frame.loc[frame.index[:5], 'a'] = np.nan
In [12]: frame.loc[frame.index[5:10], 'b'] = np.nan
In [13]: frame.cov()
Out[13]:
a b c
a 1.123670 -0.412851 0.018169
b -0.412851 1.154141 0.305260
c 0.018169 0.305260 1.301149
In [14]: frame.cov(min_periods=12)
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https://pandas.pydata.org/pandas-docs/version/0.25.0/user_guide/computation.html