code: def ccovf(x, y, adjusted=True, demean=True, fft=True):
      """
      Calculate the cross-covariance between two series.
  
      Parameters
      ----------
      x, y : array_like
         The time series data to use in the calculation.
      adjusted : bool, optional
         If True, then denominators for cross-covariance are n-k, otherwise n.
      demean : bool, optional
          Flag indicating whether to demean x and y.
      fft : bool, default True
          If True, use FFT convolution.  This method should be preferred
          for long time series.
  
      Returns
      -------
      ndarray
          The estimated cross-covariance function: the element at index k
          is the covariance between {x[k], x[k+1], ..., x[n]} and {y[0], y[1], ..., y[m-k]},
          where n and m are the lengths of x and y, respectively.
      """
      x = array_like(x, "x")
      y = array_like(y, "y")
      adjusted = bool_like(adjusted, "adjusted")
      demean = bool_like(demean, "demean")
      fft = bool_like(fft, "fft", optional=False)
  
      n = len(x)
      if demean:
          xo = x - x.mean()
          yo = y - y.mean()
      else:
          xo = x
          yo = y
      if adjusted:
          d = np.arange(n, 0, -1)
      else:
          d = n
  
      method = "fft" if fft else "direct"
      return correlate(xo, yo, "full", method=method)[n - 1 :] / d
  
imports: from __future__ import annotations
  from statsmodels.compat.numpy import lstsq
  from statsmodels.compat.pandas import deprecate_kwarg
  from statsmodels.compat.python import Literal, lzip
  from statsmodels.compat.scipy import _next_regular
  from typing import Union
  import warnings
  import numpy
  from numpy.linalg import LinAlgError
  import pandas
  from scipy import stats
  from scipy.interpolate import interp1d
  from scipy.signal import correlate
  from statsmodels.regression.linear_model import OLS, yule_walker
  from statsmodels.tools.sm_exceptions import CollinearityWarning, InfeasibleTestError, InterpolationWarning, MissingDataError, ValueWarning
  from statsmodels.tools.tools import Bunch, add_constant
  from statsmodels.tools.validation import array_like, bool_like, dict_like, float_like, int_like, string_like
  from statsmodels.tsa._bds import bds
  from statsmodels.tsa._innovations import innovations_algo, innovations_filter
  from statsmodels.tsa.adfvalues import mackinnoncrit, mackinnonp
  from statsmodels.tsa.tsatools import add_trend, lagmat, lagmat2ds
label_desc: Use image node_id 10 for calling a global function with example usage: ccovf(x, y, adjusted, demean, fft) and returns: unknown