StandardScalerでdatetime型を含むデータをfit_transformする方法を教えていただきたい

StandardScalerを用いた関数を作ったのですが、正常に動作してくれません。解決策を教えていただきたいです。

以下のようなデータを、5日でひとまとまりとし、１日ずつずらして重ねる三次元のデータを作ろうとしていました。そこでエラーが発生してしまい、その対処法がわかりませんでした。よろしくお願いいたします。

発生している問題・エラーメッセージ

ValueError                                Traceback (most recent call last)
<ipython-input-59-c573d2a23500> in <module>
     14 num_date = 5
     15 
---> 16 X_train_t = get_standardized_t(X=X_train, num_date = num_date)
     17 X_val_t = get_standardized_t(X=X_val, num_date = num_date)
     18 X_test_t = get_standardized_t(X=X_test, num_date = num_date)

<ipython-input-59-c573d2a23500> in get_standardized_t(X, num_date)
      7         X_t = X[i:i+num_date]
      8         scaler = StandardScaler()
----> 9         X_standardized = scaler.fit_transform(X_t)
     10         X_t_list.append(X_standardized)
     11         #Numpy配列のreturn

/opt/conda/lib/python3.7/site-packages/sklearn/base.py in fit_transform(self, X, y, **fit_params)
    551         if y is None:
    552             # fit method of arity 1 (unsupervised transformation)
--> 553             return self.fit(X, **fit_params).transform(X)
    554         else:
    555             # fit method of arity 2 (supervised transformation)

/opt/conda/lib/python3.7/site-packages/sklearn/preprocessing/data.py in fit(self, X, y)
    637         # Reset internal state before fitting
    638         self._reset()
--> 639         return self.partial_fit(X, y)
    640 
    641     def partial_fit(self, X, y=None):

/opt/conda/lib/python3.7/site-packages/sklearn/preprocessing/data.py in partial_fit(self, X, y)
    661         X = check_array(X, accept_sparse=('csr', 'csc'), copy=self.copy,
    662                         estimator=self, dtype=FLOAT_DTYPES,
--> 663                         force_all_finite='allow-nan')
    664 
    665         # Even in the case of `with_mean=False`, we update the mean anyway

/opt/conda/lib/python3.7/site-packages/sklearn/utils/validation.py in check_array(array, accept_sparse, accept_large_sparse, dtype, order, copy, force_all_finite, ensure_2d, allow_nd, ensure_min_samples, ensure_min_features, warn_on_dtype, estimator)
    494             try:
    495                 warnings.simplefilter('error', ComplexWarning)
--> 496                 array = np.asarray(array, dtype=dtype, order=order)
    497             except ComplexWarning:
    498                 raise ValueError("Complex data not supported\n"

/opt/conda/lib/python3.7/site-packages/numpy/core/numeric.py in asarray(a, dtype, order)
    536 
    537     """
--> 538     return array(a, dtype, copy=False, order=order)
    539 
    540 

ValueError: could not convert string to float: '2010-12-02'

該当のソースコード

X_train データ
                  Open        High         Low       Close
Date                                                      
2013-10-01  344.312670  401.461943  403.402575  412.43153
2013-10-02  339.420133  401.431664  397.470175  400.26351

python
1
2train_data['Date'] = pd.to_datetime(train_data['Date'])
3train_data.set_index(keys='Date', inplace=True)
4
5
6#データを正規化して、5日移動平均するための３次元データを作る関数
7def standardized_t(X, num):
8    X = np.array(X)
9    X_t_list = []
10    for i in range(len(X)- num + 1):
11        X_t = X[i:i+num]
12        scaler = StandardScaler()
13        X_standardized = scaler.fit_transform(X_t)
14        X_t_list.append(X_standardized)
15    return np.array(X_t_list)
16
17num = 5
18
19X_train_t =　standardized_t(X=X_train, num = num)