code: def garch_recursion_python(
      parameters: Float64Array,
      fresids: Float64Array,
      sresids: Float64Array,
      sigma2: Float64Array,
      p: int,
      o: int,
      q: int,
      nobs: int,
      backcast: float,
      var_bounds: Float64Array,
  ) -> Float64Array:
      """
      Compute variance recursion for GARCH and related models
  
      Parameters
      ----------
      parameters : ndarray
          Model parameters
      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.
      sresids : ndarray
          Variable containing the sign of the residuals (-1.0, 0.0, 1.0)
      sigma2 : ndarray
          Conditional variances with same shape as resids
      p : int
          Number of symmetric innovations in model
      o : int
          Number of asymmetric innovations in model
      q : int
          Number of lags of the (transformed) variance in the model
      nobs : int
          Length of resids
      backcast : float
          Value to use when initializing the recursion
      var_bounds : 2-d array
          nobs by 2-element array of upper and lower bounds for conditional
          transformed variances for each time period
      """
  
      for t in range(nobs):
          loc = 0
          sigma2[t] = parameters[loc]
          loc += 1
          for j in range(p):
              if (t - 1 - j) < 0:
                  sigma2[t] += parameters[loc] * backcast
              else:
                  sigma2[t] += parameters[loc] * fresids[t - 1 - j]
              loc += 1
          for j in range(o):
              if (t - 1 - j) < 0:
                  sigma2[t] += parameters[loc] * 0.5 * backcast
              else:
                  sigma2[t] += (
                      parameters[loc]
                      * fresids[t - 1 - j]
                      * (sresids[t - 1 - j] < 0)
                  )
              loc += 1
          for j in range(q):
              if (t - 1 - j) < 0:
                  sigma2[t] += parameters[loc] * backcast
              else:
                  sigma2[t] += parameters[loc] * sigma2[t - 1 - j]
              loc += 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 6 for calling a global function with example usage: garch_recursion_python(parameters, fresids, sresids, sigma2, p, o, q, nobs, backcast, var_bounds) and returns: sigma2