code: def test_prediction_increment_pandas_noindex():
      endog = dta[2].copy()
      mod = tsa_model.TimeSeriesModel(endog)
  
      # Tests three common use cases: basic prediction, negative indexes, and
      # out-of-sample indexes.
  
      # Basic prediction: [0, end]; since there was no index and the data is
      # Pandas, the index is the generated incrementing index, and no warning is
      # issued
      start_key = 0
      end_key = None
      (
          start,
          end,
          out_of_sample,
          prediction_index,
      ) = mod._get_prediction_index(start_key, end_key)
  
      assert_equal(start, 0)
      assert_equal(end, nobs - 1)
      assert_equal(out_of_sample, 0)
      assert_equal(prediction_index.equals(mod._index), True)
  
      # Negative index: [-2, end]; since there was no index and the data is
      # Pandas, the index is the generated incrementing index, and no warning is
      # issued
      start_key = -2
      end_key = -1
      (
          start,
          end,
          out_of_sample,
          prediction_index,
      ) = mod._get_prediction_index(start_key, end_key)
  
      assert_equal(start, 3)
      assert_equal(end, 4)
      assert_equal(out_of_sample, 0)
      assert_equal(prediction_index.equals(mod._index[3:]), True)
  
      # Forecasting: [1, 5]; since there was no index and the data is
      # Pandas, the index is the generated incrementing index, and no warning is
      # issued
      start_key = 1
      end_key = nobs
      (
          start,
          end,
          out_of_sample,
          prediction_index,
      ) = mod._get_prediction_index(start_key, end_key)
  
      assert_equal(start, 1)
      assert_equal(end, 4)
      assert_equal(out_of_sample, 1)
      assert_equal(
          prediction_index.equals(pd.Index(np.arange(1, 6))), True
      )
  
imports: from statsmodels.compat.pandas import PD_LT_2_2_0, YEAR_END, is_int_index
  import warnings
  import numpy
  from numpy.testing import assert_equal, assert_raises
  import pandas
  import pytest
  from statsmodels.tools.sm_exceptions import ValueWarning
  from statsmodels.tsa.base import tsa_model
label_desc: Use image node_id 4 for calling a global function with example usage: test_prediction_increment_pandas_noindex() without return types