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我将波动率数据帧 (rvm) 与相关数据帧 (omega_tilde) 相乘以获得协方差矩阵。

rvm DataFrame（5790 行 × 10 列）：

                     NoDur  Durbl   Manuf   Enrgy   HiTec   Telcm   Shops   Hlth    Utils   Other
Date          lvl1                              
1972-11-30    NoDur  0.006660       0       0       0       0       0       0       0       0
              Durbl  0      0.00939 0       0       0       0       0       0       0       0
              Manuf  0      0       0.00803 0       0       0       0       0       0       0
              Enrgy  0      0       0       0.00851 0       0       0       0       0       0
              HiTec  0      0       0       0       0.01205 0       0       0       0       0
              Telcm  0      0       0       0       0       0.00799 0       0       0       0
              Shops  0      0       0       0       0       0       0.00795 0       0       0
              Hlth   0      0       0       0       0       0       0       0.00819 0       0
              Utils  0      0       0       0       0       0       0       0       0.00505 0
              Other  0      0       0       0       0       0       0       0       0       0.00892
1972-11-31    NoDur  0.006640       0       0       0       0       0       0       0       0
              Durbl  0      0.00943 0       0       0       0       0       0       0       0
              Manuf  0      0       0.00800 0       0       0       0       0       0       0
              Enrgy  0      0       0       0.00837 0       0       0       0       0       0
              HiTec  0      0       0       0       0.01185 0       0       0       0       0
              Telcm  0      0       0       0       0       0.00792 0       0       0       0
              Shops  0      0       0       0       0       0       0.00794 0       0       0
              Hlth   0      0       0       0       0       0       0       0.00804 0       0
              Utils  0      0       0       0       0       0       0       0       0.00504 0
              Other  0      0       0       0       0       0       0       0       0       0.00889

omega_tilde 数据帧（5790 行 × 10 列）：

                     NoDur   Durbl   Manuf   Enrgy   HiTec   Telcm   Shops   Hlth    Utils   Other
Date        level_1                                     
2021-01-31  NoDur    1.00000 0.62369 0.87367 0.65322 0.74356 0.84011 0.77417 0.80183 0.82833 0.84094
            Durbl    0.62369 1.00000 0.69965 0.57501 0.70125 0.60104 0.68652 0.61333 0.45301 0.70556
            Manuf    0.87367 0.69965 1.00000 0.78599 0.81415 0.84477 0.80932 0.82127 0.74803 0.94673
            Enrgy    0.65322 0.57501 0.78599 1.00000 0.59940 0.67492 0.58058 0.61946 0.57830 0.81593
            HiTec    0.74356 0.70125 0.81415 0.59940 1.00000 0.75436 0.91318 0.84508 0.59302 0.81109
            Telcm    0.84011 0.60104 0.84477 0.67492 0.75436 1.00000 0.77555 0.77342 0.73186 0.85595
            Shops    0.77417 0.68652 0.80932 0.58058 0.91318 0.77555 1.00000 0.81197 0.61574 0.79932
            Hlth     0.80183 0.61333 0.82127 0.61946 0.84508 0.77342 0.81197 1.00000 0.70032 0.80875
            Utils    0.82833 0.45301 0.74803 0.57830 0.59302 0.73186 0.61574 0.70032 1.00000 0.72739
            Other    0.84094 0.70556 0.94673 0.81593 0.81109 0.85595 0.79932 0.80875 0.72739 1.00000
2021-02-28  NoDur    1.00000 0.61544 0.87041 0.64622 0.73941 0.83792 0.77075 0.79993 0.82813 0.83937
            Durbl    0.61544 1.00000 0.69464 0.55865 0.70203 0.59109 0.68265 0.60963 0.44792 0.69685 
            Manuf    0.87041 0.69464 1.00000 0.78243 0.81121 0.84189 0.80395 0.81809 0.74489 0.94605
            Enrgy    0.64622 0.55865 0.78243 1.00000 0.58911 0.67134 0.56925 0.61252 0.56865 0.81365
            HiTec    0.73941 0.70203 0.81121 0.58911 1.00000 0.74904 0.91274 0.84179 0.58973 0.80581
            Telcm    0.83792 0.59109 0.84189 0.67134 0.74904 1.00000 0.77078 0.76844 0.72814 0.85493
            Shops    0.77075 0.68265 0.80395 0.56925 0.91274 0.77078 1.00000 0.80924 0.61446 0.79342
            Hlth     0.79993 0.60963 0.81809 0.61252 0.84179 0.76844 0.80924 1.00000 0.69965 0.80394
            Utils    0.82813 0.44792 0.74489 0.56865 0.58973 0.72814 0.61446 0.69965 1.00000 0.72542
            Other    0.83937 0.69685 0.94605 0.81365 0.80581 0.85493 0.79342 0.80394 0.72542 1.00000

我试过的代码：

sigma_tilde = omega_tilde.groupby(level='Date').apply(lambda g: rvm_diag.loc[g.name].dot(g.values@(rvm_diag.loc[g.name])))

我得到的错误：

ValueError: matrices are not aligned

编辑：我还尝试了以下方法：

 reshaped = omega_tilde.values.reshape(omega_tilde.index.levels[0].nunique(), omega_tilde.index.levels[1].nunique(), omega_tilde.shape[-1])
 np.einsum('ijk,ik->ijk', rvm_diag.values, np.einsum('ijk,ik->ij', reshaped, rvm_diag.values))

这里的错误：

 ValueError: operands could not be broadcast together with remapped shapes [original->remapped]: (579,10,10)->(579,10,10) (5790,10)->(5790,newaxis,10)

我想要的输出与 omega_tilde DataFrame 的格式相同，因此每天都有一个矩阵。

任何帮助表示赞赏。谢谢！

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1 回答 1

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为矩阵乘法添加了为您提供ValueError: matrices are not aligned刚刚需要的代码，您可以将其用于两个乘法步骤，以便返回一个 DataFrame。.values@

sigma_tilde = (
    omega_tilde
    .groupby(level='Date')
    .apply(lambda g: rvm.loc[g.name].values@(g.values@(rvm.loc[g.name]))
)

# additional step to change the second level of index
sigma_tilde.index.set_levels(omega_tilde.columns, 1, inplace=True)

在一个较小的示例中（上面 DF 的左上角 3x3 象限，但两个月的值相同，两个 DF 使用相同的两个月）：

omega_tilde = pd.DataFrame(
    np.array(
        [[1.00000, 0.62369, 0.87367],
         [0.62369, 1.00000, 0.69965],
         [0.87367, 0.69965, 1.00000],
         [1.00000, 0.62369, 0.87367],
         [0.62369, 1.00000, 0.69965],
         [0.87367, 0.69965, 1.00000]]
    ),
    index = pd.MultiIndex.from_arrays(
        [[pd.Timestamp('2021-01-31'), pd.Timestamp('2021-01-31'),
          pd.Timestamp('2021-01-31'), pd.Timestamp("2021-02-28"),
          pd.Timestamp("2021-02-28"), pd.Timestamp("2021-02-28")],
         ['NoDur', 'Durbl', 'Manuf']*2],
         names=['Date', 'level_1']
    ),
    columns = ['NoDur', 'Durbl', 'Manuf']
)

rvm = pd.DataFrame(
    np.array(
        [[0.00666, 0, 0],
         [0, 0.00939, 0],
         [0, 0, 0.00803],
         [0.00666, 0, 0],
         [0, 0.00939, 0],
         [0, 0, 0.00803]]
    ),
    index = pd.MultiIndex.from_arrays(
        [[pd.Timestamp('2021-01-31'), pd.Timestamp('2021-01-31'),
          pd.Timestamp('2021-01-31'), pd.Timestamp("2021-02-28"),
          pd.Timestamp("2021-02-28"), pd.Timestamp("2021-02-28")],
         ['NoDur', 'Durbl', 'Manuf']*2],
         names=['Date', 'level_1']
    ),
    columns = ['NoDur', 'Durbl', 'Manuf']
)

乘法代码将产生：

             level_1       NoDur       Durbl       Manuf
2021-01-31     NoDur    0.000044    0.000039    0.000047
               Durbl    0.000039    0.000088    0.000053
               Manuf    0.000047    0.000053    0.000064
2021-02-28     NoDur    0.000044    0.000039    0.000047
               Durbl    0.000039    0.000088    0.000053
               Manuf    0.000047    0.000053    0.000064
于 2021-04-21T21:09:35.023 回答