code: def pred_autocorr(
      pred: pd.Series, lag=1, inst_col="instrument", date_col="datetime"
  ):
      """pred_autocorr.
  
      Limitation:
      - If the datetime is not sequential densely, the correlation will be calulated based on adjacent dates. (some users may expected NaN)
  
      :param pred: pd.Series with following format
                  instrument  datetime
                  SH600000    2016-01-04   -0.000403
                              2016-01-05   -0.000753
                              2016-01-06   -0.021801
                              2016-01-07   -0.065230
                              2016-01-08   -0.062465
      :type pred: pd.Series
      :param lag:
      """
      if isinstance(pred, pd.DataFrame):
          pred = pred.iloc[:, 0]
          get_module_logger("pred_autocorr").warning(
              f"Only the first column in {pred.columns} of `pred` is kept"
          )
      pred_ustk = pred.sort_index().unstack(inst_col)
      corr_s = {}
      for (idx, cur), (_, prev) in zip(
          pred_ustk.iterrows(), pred_ustk.shift(lag).iterrows()
      ):
          corr_s[idx] = cur.corr(prev)
      corr_s = pd.Series(corr_s).sort_index()
      return corr_s
  
file_path: qlib/qlib/contrib/eva/alpha.py
imports: import pandas
  from typing import Tuple
  from qlib import get_module_logger
  from qlib.utils.paral import complex_parallel, DelayedDict
  from joblib import Parallel, delayed
label_desc: Use image node_id 3 for calling a global function with example usage: pred_autocorr(pred, lag, inst_col, date_col) and returns: corr_s