code: def test_vectorization_series_to_panel(mtype, backend):
      """Test that forecaster vectorization works for Panel data.
  
      This test passes Panel data to the ARIMA forecaster which internally has an
      implementation for Series only, so the BaseForecaster has to vectorize.
      """
      n_instances = 10
  
      y = _make_panel(
          n_instances=n_instances, random_state=42, return_mtype=mtype
      )
  
      f = ARIMA()
      f.set_config(**backend.copy())
      y_pred = f.fit(y).predict([1, 2, 3])
      valid, _, metadata = check_is_mtype(
          y_pred, mtype, return_metadata=True, msg_return_dict="list"
      )
  
      msg = (
          f"vectorization of forecasters does not work for test example "
          f"of mtype {mtype}, using the ARIMA forecaster"
      )
  
      assert valid, msg
  
      y_pred_instances = metadata["n_instances"]
      msg = (
          f"vectorization test produces wrong number of instances "
          f"expected {n_instances}, found {y_pred_instances}"
      )
  
      assert y_pred_instances == n_instances, msg
  
      y_pred_equal_length = metadata["is_equal_length"]
      msg = (
          "vectorization test produces non-equal length Panel forecast, should be "
          "equal length, and length equal to the forecasting horizon [1, 2, 3]"
      )
      assert y_pred_equal_length, msg
  
      cutoff_expected = get_cutoff(y)
      msg = (
          "estimator in vectorization test does not properly update cutoff, "
          f"expected {cutoff_expected}, but found {f.cutoff}"
      )
      assert f.cutoff == cutoff_expected, msg
  
imports: from functools import reduce
  from operator import mul
  import numpy
  import pandas
  import pytest
  from pandas.testing import assert_series_equal
  from sktime.datatypes import check_is_mtype, convert
  from sktime.datatypes._utilities import get_cutoff, get_window
  from sktime.forecasting.arima import ARIMA
  from sktime.forecasting.naive import NaiveForecaster
  from sktime.forecasting.theta import ThetaForecaster
  from sktime.forecasting.var import VAR
  from sktime.utils._testing.hierarchical import _make_hierarchical
  from sktime.utils._testing.panel import _make_panel
  from sktime.utils._testing.series import _make_series
  from sktime.utils.parallel import _get_parallel_test_fixtures
  from sktime.utils.validation._dependencies import _check_estimator_deps
label_desc: Use image node_id 1 for calling a global function with example usage: test_vectorization_series_to_panel(mtype, backend) without return types