code: def test_simulate_arx(form):
      normal = Normal(seed=np.random.RandomState(0))
      gim = ARCHInMean(
          SP500,
          constant=False,
          lags=2,
          volatility=GARCH(),
          distribution=normal,
          x=X,
          form=form,
      )
      res = gim.fit(disp="off")
      sim = gim.simulate(
          res.params, 1000, x=X.iloc[:1500], initial_value=0.0
      )
      assert sim.shape == (1000, 3)
      assert "data" in sim
      assert "volatility" in sim
      assert "errors" in sim
      gim.simulate(
          res.params, 1000, x=X.iloc[:1500], initial_value=np.zeros(2)
      )
  
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 10 for calling a global function with example usage: test_simulate_arx(form) without return types