code: def add_lag(x, col=None, lags=1, drop=False, insert=True):
      """
      Returns an array with lags included given an array.
  
      Parameters
      ----------
      x : array_like
          An array or NumPy ndarray subclass. Can be either a 1d or 2d array with
          observations in columns.
      col : int or None
          `col` can be an int of the zero-based column index. If it's a
          1d array `col` can be None.
      lags : int
          The number of lags desired.
      drop : bool
          Whether to keep the contemporaneous variable for the data.
      insert : bool or int
          If True, inserts the lagged values after `col`. If False, appends
          the data. If int inserts the lags at int.
  
      Returns
      -------
      array : ndarray
          Array with lags
  
      Examples
      --------
  
      >>> import statsmodels.api as sm
      >>> data = sm.datasets.macrodata.load()
      >>> data = data.data[['year','quarter','realgdp','cpi']]
      >>> data = sm.tsa.add_lag(data, 'realgdp', lags=2)
  
      Notes
      -----
      Trims the array both forward and backward, so that the array returned
      so that the length of the returned array is len(`X`) - lags. The lags are
      returned in increasing order, ie., t-1,t-2,...,t-lags
      """
      lags = int_like(lags, "lags")
      drop = bool_like(drop, "drop")
      x = array_like(x, "x", ndim=2)
      if col is None:
          col = 0
  
      # handle negative index
      if col < 0:
          col = x.shape[1] + col
      if x.ndim == 1:
          x = x[:, None]
      contemp = x[:, col]
  
      if insert is True:
          ins_idx = col + 1
      elif insert is False:
          ins_idx = x.shape[1]
      else:
          if insert < 0:  # handle negative index
              insert = x.shape[1] + insert + 1
          if insert > x.shape[1]:
              insert = x.shape[1]
  
              warnings.warn(
                  "insert > number of variables, inserting at the"
                  " last position",
                  ValueWarning,
              )
          ins_idx = insert
  
      ndlags = lagmat(contemp, lags, trim="Both")
      first_cols = lrange(ins_idx)
      last_cols = lrange(ins_idx, x.shape[1])
      if drop:
          if col in first_cols:
              first_cols.pop(first_cols.index(col))
          else:
              last_cols.pop(last_cols.index(col))
      return np.column_stack(
          (x[lags:, first_cols], ndlags, x[lags:, last_cols])
      )
  
imports: from __future__ import annotations
  from statsmodels.compat.python import Literal, lrange
  import warnings
  import numpy
  import pandas
  from pandas import DataFrame
  from pandas.tseries import offsets
  from pandas.tseries.frequencies import to_offset
  from statsmodels.tools.data import _is_recarray, _is_using_pandas
  from statsmodels.tools.sm_exceptions import ValueWarning
  from statsmodels.tools.typing import NDArray
  from statsmodels.tools.validation import array_like, bool_like, int_like, string_like
label_desc: Use image node_id 2 for calling a global function with example usage: add_lag(x, col, lags, drop, insert) and returns: np