>> v2 = [3, 4, 4, 4, 8]
        >>> # numpy returns a 2X2 array, the correlation coefficient
        >>> # is the number at entry [0][1]
        >>> print(f"{{np.corrcoef(v1[:-1], v2[:-1])[0][1]:.6f}}")
        0.333333
        >>> print(f"{{np.corrcoef(v1[1:], v2[1:])[0][1]:.6f}}")
        0.916949
        >>> s1 = pd.Series(v1)
        >>> s2 = pd.Series(v2)
        >>> s1.rolling(4).corr(s2)
        0         NaN
        1         NaN
        2         NaN
        3    0.333333
        4    0.916949
        dtype: float64

        The below example shows a similar rolling calculation on a
        DataFrame using the pairwise option.

        >>> matrix = np.array([[51., 35.], [49., 30.], [47., 32.],        [46., 31.], [50., 36.]])
        >>> print(np.corrcoef(matrix[:-1,0], matrix[:-1,1]).round(7))
        [[1.         0.6263001]
         [0.6263001  1.       ]]
        >>> print(np.corrcoef(matrix[1:,0], matrix[1:,1]).round(7))
        [[1.         0.5553681]
         [0.5553681  1.        ]]
        >>> df = pd.DataFrame(matrix, columns=['X','Y'])
        >>> df
              X     Y
        0  51.0  35.0
        1  49.0  30.0
        2  47.0  32.0
        3  46.0  31.0
        4  50.0  36.0
        >>> df.rolling(4).corr(pairwise=True)
                    X         Y
        0 X       NaN       NaN
          Y       NaN       NaN
        1 X       NaN       NaN
          Y       NaN       NaN
        2 X       NaN       NaN
          Y       NaN       NaN
        3 X  1.000000  0.626300
          Y  0.626300  1.000000
        4 X  1.000000  0.555368
          Y  0.555368  1.000000
        Z