code: def test_invalid_init(data):
      with pytest.raises(
          ValueError, match="lags must be a non-negative"
      ):
          ARDL(data.y, -1)
      with pytest.raises(
          ValueError, match="All values in lags must be positive"
      ):
          ARDL(data.y, [-1, 1, 2])
      with pytest.raises(
          ValueError, match="All values in lags must be positive"
      ):
          ARDL(data.y, [1, 2, 2, 3])
      with pytest.raises(ValueError, match="hold_back must be "):
          ARDL(data.y, 3, data.x, 4, hold_back=3)
  
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 35 for calling a global function with example usage: test_invalid_init(data) without return types