code: def test_forecast_date(data):
      res = ARDL(data.y, 3).fit()
      numeric = res.forecast(12)
      date = res.forecast("1990-07-01")
      assert_allclose(numeric, date)
      assert_index_equal(numeric.index, date.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 43 for calling a global function with example usage: test_forecast_date(data) without return types