code: def test_reindex(model_spec, reindex, first_obs, last_obs):
      reindex_dim = (
          SP500.shape[0] - last_obs + 1 if last_obs is not None else 1
      )
      dim0 = SP500.shape[0] if reindex else reindex_dim
      res = model_spec.fit(
          disp="off", first_obs=first_obs, last_obs=last_obs
      )
      fcast = res.forecast(horizon=1, reindex=reindex)
      assert fcast.mean.shape == (dim0, 1)
      fcast = res.forecast(
          horizon=2,
          method="simulation",
          simulations=25,
          reindex=reindex,
      )
      assert fcast.mean.shape == (dim0, 2)
      fcast = res.forecast(
          horizon=2, method="bootstrap", simulations=25, reindex=reindex
      )
      assert fcast.mean.shape == (dim0, 2)
      assert fcast.simulations.values.shape == (dim0, 25, 2)
      with pytest.raises(ValueError, match="horizon must be"):
          res.forecast(horizon=0, reindex=reindex)
  
imports: import datetime
  from itertools import product
  import numpy
  from numpy.random import RandomState
  from numpy.testing import assert_allclose
  import pandas
  from pandas.testing import assert_frame_equal
  import pytest
  from arch.data import sp500
  from arch.tests.univariate.test_variance_forecasting import preserved_state
  from arch.univariate import APARCH, ARX, EGARCH, FIGARCH, GARCH, HARCH, HARX, ConstantMean, ConstantVariance, EWMAVariance, MIDASHyperbolic, RiskMetrics2006, ZeroMean, arch_model
  from arch.univariate.mean import _ar_forecast, _ar_to_impulse
label_desc: Use image node_id 3 for calling a global function with example usage: test_reindex(model_spec, reindex, first_obs, last_obs) without return types