code: def test_x_exceptions():
      res = ARX(SP500, lags=1).fit(disp="off")
      with pytest.raises(TypeError, match="x is not None but"):
          res.forecast(x=SP500)
      x = SP500.copy()
      x[:] = np.random.standard_normal(SP500.shape)
      x.name = "Exog"
      res = ARX(SP500, lags=1, x=x).fit(disp="off")
      with pytest.raises(TypeError, match="x is None but the model"):
          res.forecast()
      res = ARX(SP500, lags=1, x=x).fit(disp="off")
      with pytest.raises(ValueError, match="x must have the same"):
          res.forecast(x={})
      with pytest.raises(ValueError, match="x must have the same"):
          res.forecast(x={"x0": x, "x1": x})
      with pytest.raises(KeyError, match="The keys of x must exactly"):
          res.forecast(x={"z": x})
      with pytest.raises(
          ValueError, match="The arrays contained in the dictionary"
      ):
          _x = np.asarray(x).reshape((1, x.shape[0], 1))
          res.forecast(x={"Exog": _x})
      x2 = pd.concat([x, x], axis=1)
      x2.columns = ["x0", "x1"]
      x2.iloc[:, 1] = np.random.standard_normal(SP500.shape)
      res = ARX(SP500, lags=1, x=x2).fit(disp="off")
      with pytest.raises(
          ValueError, match="The shapes of the arrays contained"
      ):
          res.forecast(x={"x0": x2.iloc[:, 0], "x1": x2.iloc[10:, 1:]})
      with pytest.raises(
          ValueError, match="1- and 2-dimensional x values"
      ):
          res.forecast(x=x2)
      with pytest.raises(
          ValueError, match="The leading dimension of x"
      ):
          _x2 = np.asarray(x2)
          _x2 = _x2.reshape((1, -1, 2))
          res.forecast(x=_x2)
      with pytest.raises(
          ValueError, match="The number of values passed"
      ):
          res.forecast(x=np.empty((2, SP500.shape[0], 3)))
      with pytest.raises(
          ValueError, match="The shape of x does not satisfy the"
      ):
          res.forecast(x=np.empty((2, SP500.shape[0] // 2, 1)))
  
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 10 for calling a global function with example usage: test_x_exceptions() without return types