code: def test_naive_predict_interval_against_R_naive(
      strategy, sp, lower, upper
  ):
      """Checks naive prediction interval computations.
  
      Compare prediction interval results with R implementation in [1]_.
  
      Note:
      - Seasonality is not applicable to "mean" strategy in R.
      - Argument "window_length" is not available in R.
  
      References
      ----------
      .. [1] https://github.com/robjhyndman/forecast/blob/master/R/naive.R
      """
      n_timepoints = 100000
      mu, sigma = 0.0, 10.0
      fake_idx = pd.date_range(
          "1980", periods=n_timepoints + 1, freq="H"
      )
      np.random.seed(42)
      y = pd.Series(
          np.random.normal(mu, sigma, size=n_timepoints),
          index=fake_idx[:-1],
      )
  
      h = list(range(1, 6))
      coverage = 0.90
      forecaster = NaiveForecaster(strategy, sp=sp)
      y_pred_ints = forecaster.fit(y).predict_interval(
          fh=h, coverage=coverage
      )
  
      expected = pd.DataFrame(
          columns=pd.MultiIndex.from_product(
              [[0], [coverage], ["lower", "upper"]]
          ),
          index=y_pred_ints.index,
      )
  
      expected[(0, coverage, "lower")] = lower
      expected[(0, coverage, "upper")] = upper
  
      pd.testing.assert_frame_equal(y_pred_ints, expected)
  
imports: import numpy
  import pandas
  import pytest
  from sktime.datatypes._utilities import get_cutoff
  from sktime.forecasting.base import ForecastingHorizon
  from sktime.forecasting.naive import NaiveForecaster
  from sktime.forecasting.tests._config import TEST_OOS_FHS, TEST_SPS, TEST_WINDOW_LENGTHS_INT
  from sktime.utils._testing.forecasting import _assert_correct_pred_time_index
  from sktime.utils.validation.forecasting import check_fh
label_desc: Use image node_id 12 for calling a global function with example usage: test_naive_predict_interval_against_R_naive(strategy, sp, lower, upper) without return types