code: def test_prediction_replacements(data, fixed):
      res = ARDL(data.y, 4, data.x, [1, 3]).fit()
      direct = res.predict()
      alt = res.predict(exog=data.x)
      assert_allclose(direct, alt)
      assert_index_equal(direct.index, alt.index)
  
      res = ARDL(data.y, 4, data.x, [1, 3], fixed=fixed).fit()
      direct = res.predict()
      alt = res.predict(fixed=fixed)
      assert_allclose(direct, alt)
      assert_index_equal(direct.index, alt.index)
  
imports: from typing import NamedTuple
  import numpy
  from numpy.testing import assert_allclose
  import pandas
  from pandas.testing import assert_index_equal
  import pytest
  from statsmodels.datasets import danish_data
  from statsmodels.iolib.summary import Summary
  from statsmodels.tools.sm_exceptions import SpecificationWarning
  from statsmodels.tsa.ar_model import AutoReg
  from statsmodels.tsa.ardl.model import ARDL, UECM, ARDLResults, ardl_select_order
  from statsmodels.tsa.deterministic import DeterministicProcess
label_desc: Use image node_id 38 for calling a global function with example usage: test_prediction_replacements(data, fixed) without return types