# pandas.DataFrame.cov¶

DataFrame.cov(min_periods=None, ddof=1)[source]

Compute pairwise covariance of columns, excluding NA/null values.

Compute the pairwise covariance among the series of a DataFrame. The returned data frame is the covariance matrix of the columns of the DataFrame.

Both NA and null values are automatically excluded from the calculation. (See the note below about bias from missing values.) A threshold can be set for the minimum number of observations for each value created. Comparisons with observations below this threshold will be returned as NaN.

This method is generally used for the analysis of time series data to understand the relationship between different measures across time.

Parameters
min_periodsint, optional

Minimum number of observations required per pair of columns to have a valid result.

ddofint, default 1

Delta degrees of freedom. The divisor used in calculations is N - ddof, where N represents the number of elements.

New in version 1.1.0.

Returns
DataFrame

The covariance matrix of the series of the DataFrame.

Series.cov

Compute covariance with another Series.

core.window.ExponentialMovingWindow.cov

Exponential weighted sample covariance.

core.window.Expanding.cov

Expanding sample covariance.

core.window.Rolling.cov

Rolling sample covariance.

Notes

Returns the covariance matrix of the DataFrame’s time series. The covariance is normalized by N-ddof.

For DataFrames that have Series that are missing data (assuming that data is missing at random) the returned covariance matrix will be an unbiased estimate of the variance and covariance between the member Series.

However, for many applications this estimate may not be acceptable because the estimate covariance matrix is not guaranteed to be positive semi-definite. This could lead to estimate correlations having absolute values which are greater than one, and/or a non-invertible covariance matrix. See Estimation of covariance matrices for more details.

Examples

>>> df = pd.DataFrame([(1, 2), (0, 3), (2, 0), (1, 1)],
...                   columns=['dogs', 'cats'])
>>> df.cov()
dogs      cats
dogs  0.666667 -1.000000
cats -1.000000  1.666667

>>> np.random.seed(42)
>>> df = pd.DataFrame(np.random.randn(1000, 5),
...                   columns=['a', 'b', 'c', 'd', 'e'])
>>> df.cov()
a         b         c         d         e
a  0.998438 -0.020161  0.059277 -0.008943  0.014144
b -0.020161  1.059352 -0.008543 -0.024738  0.009826
c  0.059277 -0.008543  1.010670 -0.001486 -0.000271
d -0.008943 -0.024738 -0.001486  0.921297 -0.013692
e  0.014144  0.009826 -0.000271 -0.013692  0.977795


Minimum number of periods

This method also supports an optional min_periods keyword that specifies the required minimum number of non-NA observations for each column pair in order to have a valid result:

>>> np.random.seed(42)
>>> df = pd.DataFrame(np.random.randn(20, 3),
...                   columns=['a', 'b', 'c'])
>>> df.loc[df.index[:5], 'a'] = np.nan
>>> df.loc[df.index[5:10], 'b'] = np.nan
>>> df.cov(min_periods=12)
a         b         c
a  0.316741       NaN -0.150812
b       NaN  1.248003  0.191417
c -0.150812  0.191417  0.895202