code: def test_garch_no_lagged_vol(setup):
      garch = GARCH(p=1, o=1, q=0)
      sv = garch.starting_values(setup.resids)
      assert_equal(sv.shape[0], garch.num_params)
  
      bounds = garch.bounds(setup.resids)
      v = np.mean(setup.resids**2)
      assert_allclose(bounds[0], (1.0e-8 * v, 10.0 * v))
      assert_equal(bounds[1], (0.0, 1.0))
      assert_equal(bounds[2], (-1.0, 2.0))
  
      backcast = garch.backcast(setup.resids)
      parameters = np.array([0.5, 0.25, 0.5])
      var_bounds = garch.variance_bounds(setup.resids)
  
      garch.compute_variance(
          parameters, setup.resids, setup.sigma2, backcast, var_bounds
      )
      cond_var_direct = np.zeros_like(setup.sigma2)
      rec.garch_recursion(
          parameters,
          setup.resids**2.0,
          np.sign(setup.resids),
          cond_var_direct,
          1,
          1,
          0,
          setup.t,
          backcast,
          var_bounds,
      )
      assert_allclose(setup.sigma2, cond_var_direct)
  
      a, b = garch.constraints()
      a_target = np.vstack((np.eye(3), np.array([[0, -1.0, -0.5]])))
      a_target[2, 1] = 1.0
      b_target = np.array([0.0, 0.0, 0.0, -1.0])
      assert_array_equal(a, a_target)
      assert_array_equal(b, b_target)
      state = setup.rng.get_state()
      rng = Normal(seed=RandomState())
      rng.generator.set_state(state)
      sim_data = garch.simulate(parameters, setup.t, rng.simulate([]))
      setup.rng.set_state(state)
      e = setup.rng.standard_normal(setup.t + 500)
      initial_value = 1.0
      sigma2 = np.zeros(setup.t + 500)
      data = np.zeros(setup.t + 500)
      for t in range(setup.t + 500):
          sigma2[t] = parameters[0]
          shock = initial_value if t == 0 else data[t - 1] ** 2.0
          sigma2[t] += parameters[1] * shock
          shock = (
              0.5 * initial_value
              if t == 0
              else (data[t - 1] ** 2.0) * (data[t - 1] < 0)
          )
          sigma2[t] += parameters[2] * shock
          data[t] = e[t] * np.sqrt(sigma2[t])
      data = data[500:]
      sigma2 = sigma2[500:]
      assert_almost_equal(data - sim_data[0] + 1.0, np.ones_like(data))
      assert_almost_equal(sigma2 / sim_data[1], np.ones_like(sigma2))
  
      assert_equal(garch.p, 1)
      assert_equal(garch.o, 1)
      assert_equal(garch.q, 0)
      assert_equal(garch.num_params, 3)
      assert_equal(garch.name, "GJR-GARCH")
  
imports: import types
  from typing import NamedTuple
  import warnings
  import numpy
  from numpy.random import RandomState
  from numpy.testing import assert_allclose, assert_almost_equal, assert_array_equal, assert_equal
  import pytest
  from scipy.special import gamma, gammaln
  from arch.univariate import ZeroMean
  from arch.univariate.distribution import Normal, SkewStudent, StudentsT
  import arch.univariate.recursions_python
  from arch.univariate.volatility import APARCH, ARCH, EGARCH, FIGARCH, GARCH, HARCH, ConstantVariance, EWMAVariance, FixedVariance, MIDASHyperbolic, RiskMetrics2006
  from arch.utility.exceptions import InitialValueWarning
label_desc: Use image node_id 9 for calling a global function with example usage: test_garch_no_lagged_vol(setup) without return types