code: def test_arch_1_forecast(self):
      t = self.t
      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)
      forecast = vol.forecast(params, self.resid, backcast, var_bounds)
      expected = np.empty((t, 1))
      expected.fill(np.nan)
      expected[-1] = params[0] + params[1] * self.resid[-1] ** 2
      assert_allclose(forecast.forecasts, expected[-1:])
      assert forecast.forecast_paths is None
      assert forecast.shocks is None
  
      forecast = vol.forecast(
          params, self.resid, backcast, var_bounds, horizon=5
      )
      assert forecast.forecasts.shape == (1, 5)
      assert np.all(np.isfinite(forecast.forecasts))
      assert forecast.forecast_paths is None
      assert forecast.shocks is None
      expected = np.zeros(5)
      expected[0] = params[0] + params[1] * self.resid[-1] ** 2
      for i in range(1, 5):
          expected[i] = params[0] + params[1] * expected[i - 1]
      assert_allclose(forecast.forecasts[-1], expected)
  
      forecast = vol.forecast(
          params, self.resid, backcast, var_bounds, start=0
      )
      assert forecast.forecasts.shape == (1000, 1)
      assert np.all(np.isfinite(forecast.forecasts))
      assert forecast.forecast_paths is None
      assert forecast.shocks is None
      expected = params[0] + params[1] * self.resid**2
      expected.shape = (1000, 1)
      assert_allclose(forecast.forecasts, expected)
  
      forecast = vol.forecast(
          params, self.resid, backcast, var_bounds, start=0, horizon=3
      )
      assert forecast.forecasts.shape == (1000, 3)
      assert np.all(np.isfinite(forecast.forecasts))
      assert forecast.forecast_paths is None
      assert forecast.shocks is None
      expected = np.zeros((1000, 3))
      expected[:, 0] = params[0] + params[1] * self.resid**2
      for i in range(1, 3):
          expected[:, i] = params[0] + params[1] * expected[:, i - 1]
      assert_allclose(forecast.forecasts, expected)
  
      forecast = vol.forecast(
          params, self.resid, backcast, var_bounds, start=100, horizon=3
      )
      assert_allclose(forecast.forecasts, expected[100:])
      with pytest.raises(
          ValueError, match="horizon must be an integer >= 1"
      ):
          vol.forecast(
              params,
              self.resid,
              backcast,
              var_bounds,
              start=0,
              horizon=0,
          )
  
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 3 for calling the TestVarianceForecasts obj's underlying member method code with example usage: obj.test_arch_1_forecast() without return types