code: def _generate_vmd_testdata(T=1000, f_1=2, f_2=24, f_3=288, noise=0.1):
      """Generate test data for VMD tests.
  
      Based on example of DaneLyttinen in #5128
  
      Parameters
      ----------
      T : int
          length of time series
      f_1 : int
      f_2 : int
      f_3 : int
          center frequencies of components
          f_i = frequency of component i
      noise : float
          noise level
      """
      # Time Domain 0 to T
      T = 1000
      t = np.arange(1, T + 1) / T
  
      # modes
      v_1 = np.cos(2 * np.pi * f_1 * t)
      v_2 = 1 / 4 * (np.cos(2 * np.pi * f_2 * t))
      v_3 = 1 / 16 * (np.cos(2 * np.pi * f_3 * t))
  
      f = v_1 + v_2 + v_3 + noise * np.random.randn(v_1.size)
  
      return pd.DataFrame(data={"y": f})
  
imports: import numpy
  import pandas
  from sktime.forecasting.compose import TransformedTargetForecaster
  from sktime.forecasting.trend import TrendForecaster
  from sktime.transformations.series.vmd import VmdTransformer
label_desc: Use image node_id 1 for calling a global function with example usage: _generate_vmd_testdata(T, f_1, f_2, f_3, noise) and returns: pd