code: def test_arch_1_forecast_simulation(self):
      dist = Normal(seed=self.rng)
      rng = dist.simulate([])
      vol = GARCH(p=1, o=0, q=0)
      params = np.array([10.0, 0.4])
      backcast = vol.backcast(self.resid)
      var_bounds = vol.variance_bounds(self.resid)
  
      with preserved_state(self.rng):
          forecast = vol.forecast(
              params,
              self.resid,
              backcast,
              var_bounds,
              horizon=1,
              method="simulation",
              rng=rng,
          )
      assert forecast.forecasts.shape == (1, 1)
      assert forecast.forecast_paths.shape == (1, 1000, 1)
      assert forecast.shocks.shape == (1, 1000, 1)
      assert np.all(np.isfinite(forecast.forecasts))
      assert np.all(np.isfinite(forecast.forecast_paths))
      expected = params[0] + params[1] * self.resid[-1] ** 2.0
      assert_allclose(forecast.forecasts[-1], expected)
      assert_allclose(
          forecast.forecast_paths[-1], expected * np.ones((1000, 1))
      )
      assert_allclose(
          forecast.shocks[-1], np.sqrt(expected) * rng((1000, 1))
      )
  
      with preserved_state(self.rng):
          forecast = vol.forecast(
              params,
              self.resid,
              backcast,
              var_bounds,
              horizon=5,
              method="simulation",
              rng=rng,
          )
  
      paths = np.zeros((1000, 5))
      paths[:, 0] = expected
      std_shocks = rng((1000, 5))
      shocks = np.zeros((1000, 5))
      shocks[:, 0] = np.sqrt(paths[:, 0]) * std_shocks[:, 0]
      for i in range(1, 5):
          paths[:, i] = params[0] + params[1] * shocks[:, i - 1] ** 2
          shocks[:, i] = np.sqrt(paths[:, i]) * std_shocks[:, i]
  
      assert forecast.forecasts.shape == (1, 5)
      assert forecast.forecast_paths.shape == (1, 1000, 5)
      assert forecast.shocks.shape == (1, 1000, 5)
      assert np.all(np.isfinite(forecast.forecasts))
      assert np.all(np.isfinite(forecast.forecast_paths))
      assert np.all(np.isfinite(forecast.shocks))
      assert_allclose(forecast.forecasts[-1], paths.mean(0))
      assert_allclose(forecast.forecast_paths[-1], paths)
      assert_allclose(forecast.shocks[-1], shocks)
  
      with preserved_state(self.rng):
          forecast = vol.forecast(
              params,
              self.resid,
              backcast,
              var_bounds,
              horizon=5,
              start=100,
              method="simulation",
              simulations=2000,
              rng=rng,
          )
  
      paths = np.zeros((1000, 2000, 5))
      paths.fill(np.nan)
      shocks = np.zeros((1000, 2000, 5))
      shocks.fill(np.nan)
      for i in range(100, 1000):
          std_shocks = rng((2000, 5))
          paths[i, :, 0] = params[0] + params[1] * self.resid[i] ** 2.0
          shocks[i, :, 0] = np.sqrt(paths[i, :, 0]) * std_shocks[:, 0]
          for j in range(1, 5):
              paths[i, :, j] = (
                  params[0] + params[1] * shocks[i, :, j - 1] ** 2
              )
              shocks[i, :, j] = (
                  np.sqrt(paths[i, :, j]) * std_shocks[:, j]
              )
  
      assert_allclose(forecast.shocks, shocks[100:])
      assert_allclose(forecast.forecast_paths, paths[100:])
      assert_allclose(forecast.forecasts, paths[100:].mean(1))
  
imports: import numpy
  from numpy.random import RandomState
  from numpy.testing import assert_allclose
  import pandas
  import pytest
  from arch.univariate import arch_model
  from arch.univariate.distribution import Normal, StudentsT
  from arch.univariate.mean import ConstantMean
  from arch.univariate.volatility import APARCH, EGARCH, FIGARCH, GARCH, HARCH, BootstrapRng, ConstantVariance, EWMAVariance, FixedVariance, MIDASHyperbolic, RiskMetrics2006
label_desc: Use image node_id 4 for calling the TestVarianceForecasts obj's underlying member method code with example usage: obj.test_arch_1_forecast_simulation() without return types