code: def test_ar_forecasting(self):
      params = np.array([0.9])
      forecasts = _ar_forecast(
          self.zero_mean, 5, 0, 0.0, params, np.empty(0), np.empty(0)
      )
      expected = np.zeros((1000, 5))
      expected[:, 0] = 0.9 * self.zero_mean.values
      for i in range(1, 5):
          expected[:, i] = 0.9 * expected[:, i - 1]
      assert_allclose(forecasts, expected)
  
      params = np.array([0.5, -0.3, 0.2])
      forecasts = _ar_forecast(
          self.zero_mean, 5, 2, 0.0, params, np.empty(0), np.empty(0)
      )
      expected = np.zeros((998, 8))
      expected[:, 0] = self.zero_mean.iloc[0:-2]
      expected[:, 1] = self.zero_mean.iloc[1:-1]
      expected[:, 2] = self.zero_mean.iloc[2:]
      for i in range(3, 8):
          expected[:, i] = (
              0.5 * expected[:, i - 1]
              - 0.3 * expected[:, i - 2]
              + 0.2 * expected[:, i - 3]
          )
      fill = np.empty((2, 5))
      fill.fill(np.nan)
      expected = np.concatenate((fill, expected[:, 3:]))
      assert_allclose(forecasts, expected[2:])
  
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 2 for calling the TestForecasting obj's underlying member method code with example usage: obj.test_ar_forecasting() without return types