code: def figarch_recursion_python(
      parameters: Float64Array,
      fresids: Float64Array,
      sigma2: Float64Array,
      p: int,
      q: int,
      nobs: int,
      trunc_lag: int,
      backcast: float,
      var_bounds: Float64Array,
  ) -> Float64Array:
      """
      Parameters
      ----------
      parameters : ndarray
          Model parameters of the form (omega, phi, d, beta) where omega is the
          intercept, d is the fractional integration coefficient and phi and beta
          are parameters of the volatility process.
      fresids : ndarray
          Absolute value of residuals raised to the power in the model.  For
          example, in a standard GARCH model, the power is 2.0.
      sigma2 : ndarray
          Conditional variances with same shape as resids
      p : int
          0 or 1 to indicate whether the model contains phi
      q : int
          0 or 1 to indicate whether the model contains beta
      nobs : int
          Length of resids
      trunc_lag : int
          Truncation lag for the ARCH approximations
      backcast : float
          Value to use when initializing the recursion
      var_bounds : ndarray
          nobs by 2-element array of upper and lower bounds for conditional
          variances for each time period
  
      Returns
      -------
      sigma2 : ndarray
          Conditional variances
      """
  
      omega = parameters[0]
      beta = parameters[1 + p + q] if q else 0.0
      omega_tilde = omega / (1 - beta)
      lam = figarch_weights(parameters[1:], p, q, trunc_lag)
      for t in range(nobs):
          bc_weight = 0.0
          for i in range(t, trunc_lag):
              bc_weight += lam[i]
          sigma2[t] = omega_tilde + bc_weight * backcast
          for i in range(min(t, trunc_lag)):
              sigma2[t] += lam[i] * fresids[t - i - 1]
          sigma2[t] = bounds_check(sigma2[t], var_bounds[t])
  
      return sigma2
  
imports: from __future__ import annotations
  from arch.compat.numba import jit
  from abc import ABCMeta, abstractmethod
  from typing import cast
  import numpy
  from scipy.special import gammaln
  from arch.typing import Float64Array, Int32Array
  from arch.utility.array import AbstractDocStringInheritor
label_desc: Use image node_id 10 for calling a global function with example usage: figarch_recursion_python(parameters, fresids, sigma2, p, q, nobs, trunc_lag, backcast, var_bounds) and returns: sigma2