code: def test_specifications():
      # Clear warnings
      structural.__warningregistry__ = {}
  
      endog = [1, 2]
  
      # Test that when nothing specified, a warning is issued and the model that
      # is fit is one with irregular=True and nothing else.
      warning = SpecificationWarning
      match = "irregular component added"
      with pytest.warns(warning, match=match):
          mod = UnobservedComponents(endog)
          assert_equal(mod.trend_specification, "irregular")
  
      # Test an invalid string trend specification
      with pytest.raises(ValueError):
          UnobservedComponents(endog, "invalid spec")
  
      # Test that if a trend component is specified without a level component,
      # a warning is issued and a deterministic level component is added
      warning = SpecificationWarning
      match = "Trend component specified without"
      with pytest.warns(warning, match=match):
          mod = UnobservedComponents(endog, trend=True, irregular=True)
          assert_equal(mod.trend_specification, "deterministic trend")
  
      # Test that if a string specification is provided, a warning is issued if
      # the boolean attributes are also specified
      trend_attributes = [
          "irregular",
          "trend",
          "stochastic_level",
          "stochastic_trend",
      ]
      for attribute in trend_attributes:
          kwargs = {attribute: True}
  
          warning = SpecificationWarning
          match = "may be overridden when the trend"
          with pytest.warns(warning, match=match):
              UnobservedComponents(
                  endog, "deterministic trend", **kwargs
              )
  
      # Test that a seasonal with period less than two is invalid
      with pytest.raises(ValueError):
          UnobservedComponents(endog, seasonal=1)
  
imports: import warnings
  import numpy
  from numpy.testing import assert_equal, assert_allclose, assert_raises
  import pandas
  import pytest
  from statsmodels.datasets import macrodata
  from statsmodels.tools.sm_exceptions import SpecificationWarning
  from statsmodels.tsa.statespace import structural
  from statsmodels.tsa.statespace.structural import UnobservedComponents
  from statsmodels.tsa.statespace.tests.results import results_structural
label_desc: Use image node_id 22 for calling a global function with example usage: test_specifications() without return types