code: def test_rescale_ar():
      # GH 632
      am = arch_model(
          None, mean="AR", lags=3, vol="GARCH", p=1, o=0, q=1
      )
      data = (
          am.simulate([10, 0.4, 0.3, 0.2, 10, 0.1, 0.85], 10000).data
          / 1000
      )
      vol = GARCH()
      mod = ARX(
          data, lags=3, constant=True, volatility=vol, rescale=True
      )
      res = mod.fit()
  
      mod_no_rs = ARX(
          100 * data,
          lags=3,
          constant=True,
          volatility=vol,
          rescale=False,
      )
      res_no_rs = mod_no_rs.fit()
      assert_allclose(
          res_no_rs.params.iloc[1:4], res.params.iloc[1:4], rtol=1e-5
      )
  
      fcasts = res.forecast(horizon=100).variance
      fcasts_no_rs = res_no_rs.forecast(horizon=100).variance
      assert_allclose(
          fcasts.iloc[0, -10:], fcasts_no_rs.iloc[0, -10:], rtol=1e-5
      )
  
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 16 for calling a global function with example usage: test_rescale_ar() without return types