code: def levinson_durbin(s, nlags=10, isacov=False):
      """
      Levinson-Durbin recursion for autoregressive processes.
  
      Parameters
      ----------
      s : array_like
          If isacov is False, then this is the time series. If iasacov is true
          then this is interpreted as autocovariance starting with lag 0.
      nlags : int, optional
          The largest lag to include in recursion or order of the autoregressive
          process.
      isacov : bool, optional
          Flag indicating whether the first argument, s, contains the
          autocovariances or the data series.
  
      Returns
      -------
      sigma_v : float
          The estimate of the error variance.
      arcoefs : ndarray
          The estimate of the autoregressive coefficients for a model including
          nlags.
      pacf : ndarray
          The partial autocorrelation function.
      sigma : ndarray
          The entire sigma array from intermediate result, last value is sigma_v.
      phi : ndarray
          The entire phi array from intermediate result, last column contains
          autoregressive coefficients for AR(nlags).
  
      Notes
      -----
      This function returns currently all results, but maybe we drop sigma and
      phi from the returns.
  
      If this function is called with the time series (isacov=False), then the
      sample autocovariance function is calculated with the default options
      (biased, no fft).
      """
      s = array_like(s, "s")
      nlags = int_like(nlags, "nlags")
      isacov = bool_like(isacov, "isacov")
  
      order = nlags
  
      if isacov:
          sxx_m = s
      else:
          sxx_m = acovf(s, fft=False)[: order + 1]  # not tested
  
      phi = np.zeros((order + 1, order + 1), "d")
      sig = np.zeros(order + 1)
      # initial points for the recursion
      phi[1, 1] = sxx_m[1] / sxx_m[0]
      sig[1] = sxx_m[0] - phi[1, 1] * sxx_m[1]
      for k in range(2, order + 1):
          phi[k, k] = (
              sxx_m[k] - np.dot(phi[1:k, k - 1], sxx_m[1:k][::-1])
          ) / sig[k - 1]
          for j in range(1, k):
              phi[j, k] = phi[j, k - 1] - phi[k, k] * phi[k - j, k - 1]
          sig[k] = sig[k - 1] * (1 - phi[k, k] ** 2)
  
      sigma_v = sig[-1]
      arcoefs = phi[1:, -1]
      pacf_ = np.diag(phi).copy()
      pacf_[0] = 1.0
      return sigma_v, arcoefs, pacf_, sig, phi
  
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 12 for calling a global function with example usage: levinson_durbin(s, nlags, isacov) and returns: sigma_v,  arcoefs,  pacf_,  sig,  phi