code: def test_loglikelihood(key, data, dtype, simple_differencing):
      """Test loglikelihood against statsmodels (with the same values for the
      model parameters)
      """
      order, seasonal_order, intercept = extract_order(key)
  
      _, y_train_cudf, _, _, _, exog_past_cudf, *_ = get_dataset(
          data, dtype
      )
  
      # Get fit reference model
      ref_fits = get_ref_fit(
          data, order, seasonal_order, intercept, dtype
      )
  
      # Create cuML model
      cuml_model = arima.ARIMA(
          endog=y_train_cudf,
          exog=exog_past_cudf,
          order=order,
          seasonal_order=seasonal_order,
          fit_intercept=intercept,
          simple_differencing=simple_differencing,
      )
  
      # Feed the parameters to the cuML model
      _statsmodels_to_cuml(
          ref_fits, cuml_model, order, seasonal_order, intercept, dtype
      )
  
      # Compute loglikelihood
      cuml_llf = cuml_model.llf
      ref_llf = np.array([ref_fit.llf for ref_fit in ref_fits])
  
      # Compare results
      np.testing.assert_allclose(
          cuml_llf, ref_llf, rtol=0.01, atol=0.01
      )
  
imports: from cuml.testing.utils import stress_param
  from cuml.internals.input_utils import input_to_host_array
  import cuml.tsa.arima
  from cuml.internals.safe_imports import gpu_only_import
  import statsmodels.api
  from sklearn.model_selection import train_test_split
  from cuml.internals.safe_imports import cpu_only_import_from
  import warnings
  import os
  import pytest
  from cuml.internals.safe_imports import cpu_only_import
label_desc: Use image node_id 13 for calling a global function with example usage: test_loglikelihood(key, data, dtype, simple_differencing) without return types