code: def test_deprecated_arguments_multivariate():
      endog = np.array(
          [[0.3, 1.4], [-0.1, 0.6], [0.2, 0.7], [0.1, 0.9], [0.5, -0.1]]
      )
  
      mod = varmax.VARMAX(endog, order=(1, 0, 0))
      mod.update([1.2, 0.5, 0.8, 0.1, -0.2, 0.5, 5.2, 0.5, 8.1])
  
      mds = np.arange(10).reshape(5, 2) / 10.0
      sds = np.arange(10).reshape(5, 2)[::-1] / 20.0
  
      # Test using deprecated `disturbance_variates`
      sim = mod.simulation_smoother()
      sim.simulate(
          measurement_disturbance_variates=mds,
          state_disturbance_variates=sds,
          initial_state_variates=np.zeros(2),
      )
      desired = sim.simulated_state[0]
  
      with pytest.warns(FutureWarning):
          sim.simulate(
              disturbance_variates=np.r_[mds.ravel(), sds.ravel()],
              initial_state_variates=np.zeros(2),
          )
      actual = sim.simulated_state[0]
  
      # Test using deprecated `pretransformed`
      sim = mod.simulation_smoother()
      sim.simulate(
          measurement_disturbance_variates=mds,
          state_disturbance_variates=sds,
          initial_state_variates=np.zeros(2),
          pretransformed_measurement_disturbance_variates=True,
          pretransformed_state_disturbance_variates=True,
      )
      desired = sim.simulated_state[0]
  
      with pytest.warns(FutureWarning):
          sim.simulate(
              measurement_disturbance_variates=mds,
              state_disturbance_variates=sds,
              pretransformed=True,
              initial_state_variates=np.zeros(2),
          )
      actual = sim.simulated_state[0]
  
      assert_allclose(actual, desired)
  
imports: import os
  import numpy
  import pandas
  from numpy.testing import assert_allclose, assert_equal
  import pytest
  from statsmodels import datasets
  from statsmodels.tsa.statespace import mlemodel, sarimax, structural, varmax
  from statsmodels.tsa.statespace.simulation_smoother import SIMULATION_STATE, SIMULATION_DISTURBANCE, SIMULATION_ALL
label_desc: Use image node_id 6 for calling a global function with example usage: test_deprecated_arguments_multivariate() without return types