code: def test_simulate():
      normal = Normal(seed=np.random.RandomState(0))
      gim = ARCHInMean(SP500, volatility=GARCH(), distribution=normal)
      res = gim.fit(disp="off")
      sim = gim.simulate(res.params, 1000)
      assert sim.shape == (1000, 3)
      assert "data" in sim
      assert "volatility" in sim
      assert "errors" in sim
      mean = sim.data - sim.errors
      vol = mean - res.params.iloc[0]
      kappa = res.params.iloc[1]
      rescaled_vol = vol / kappa
      np.testing.assert_allclose(rescaled_vol, sim.volatility)
      with pytest.raises(
          ValueError, match="initial_value has the wrong shape"
      ):
          gim.simulate(
              res.params, 1000, initial_value=np.array([0.0, 0.0])
          )
  
file_path: arch/arch/tests/univariate/test_arch_in_mean.py
imports: import numpy
  import pandas
  import pytest
  from arch.data import sp500
  from arch.univariate import ARCHInMean, Normal
  from arch.univariate.volatility import ARCH, EGARCH, FIGARCH, GARCH, HARCH, EWMAVariance, MIDASHyperbolic, RiskMetrics2006
label_desc: Use image node_id 7 for calling a global function with example usage: test_simulate() without return types