code: def test_output_backtesting_forecaster_no_exog_no_initial_train_size_with_mocked():
      """
      Test output of _backtesting_forecaster with backtesting mocked, interval no.
      Regressor is LinearRegression with lags=3, Series y is mocked, no exog,
      no initial_train_size, steps=1, ForecasterAutoreg.
      """
      expected_metric = 0.05194702533929101
      expected_predictions = pd.DataFrame(
          {
              "pred": np.array(
                  [
                      0.50394528,
                      0.53092847,
                      0.51638165,
                      0.47382814,
                      0.61996956,
                      0.47685471,
                      0.52565717,
                      0.50842469,
                      0.4925563,
                      0.55717972,
                      0.45707228,
                      0.45990822,
                      0.53762873,
                      0.5230163,
                      0.41661072,
                      0.51097738,
                      0.52448483,
                      0.48179537,
                      0.5307759,
                      0.55580453,
                      0.51780297,
                      0.53189442,
                      0.55356883,
                      0.46142853,
                      0.52517734,
                      0.46241276,
                      0.49292214,
                      0.53169102,
                      0.40448875,
                      0.55686226,
                      0.46860633,
                      0.5098154,
                      0.49041677,
                      0.48435035,
                      0.51152271,
                      0.56870534,
                      0.53226143,
                      0.49091506,
                      0.56878395,
                      0.42767269,
                      0.53335856,
                      0.48167273,
                      0.5658333,
                      0.41464667,
                      0.56733702,
                      0.5724869,
                      0.45299923,
                  ]
              )
          },
          index=pd.RangeIndex(start=3, stop=50, step=1),
      )
  
      forecaster = ForecasterAutoreg(
          regressor=LinearRegression(), lags=3
      )
      forecaster.fit(y=y)
  
      initial_train_size = None
  
      metric, backtest_predictions = _backtesting_forecaster(
          forecaster=forecaster,
          y=y,
          exog=None,
          refit=False,
          initial_train_size=initial_train_size,
          steps=1,
          metric="mean_squared_error",
          interval=None,
          n_boot=500,
          random_state=123,
          in_sample_residuals=True,
          verbose=False,
      )
  
      assert expected_metric == approx(metric)
      pd.testing.assert_frame_equal(
          expected_predictions, backtest_predictions
      )
  
imports: import pytest
  import numpy
  import pandas
  from pytest import approx
  from sklearn.linear_model import LinearRegression
  from sklearn.metrics import mean_squared_error
  from skforecast.ForecasterAutoreg import ForecasterAutoreg
  from skforecast.ForecasterAutoregCustom import ForecasterAutoregCustom
  from skforecast.ForecasterAutoregDirect import ForecasterAutoregDirect
  from skforecast.model_selection.model_selection import _backtesting_forecaster
  from .fixtures_model_selection import y
  from .fixtures_model_selection import exog
  from .fixtures_model_selection import out_sample_residuals
label_desc: Use image node_id 5 for calling a global function with example usage: test_output_backtesting_forecaster_no_exog_no_initial_train_size_with_mocked() without return types