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
This method is generally used for the analysis of time series data to understand the relationship between different measures across time.
- 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
Nrepresents the number of elements.
New in version 1.1.0.
The covariance matrix of the series of the DataFrame.
Compute covariance with another Series.
Exponential weighted sample covariance.
Expanding sample covariance.
Rolling sample covariance.
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.
>>> 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_periodskeyword 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