code: def test_cross_validation_default_value_check(
      self, ts_short, backend
  ):
      m = Prophet(stan_backend=backend)
      m.fit(ts_short)
      # Default value of initial should be equal to 3 * horizon
      df_cv1 = diagnostics.cross_validation(
          m, horizon="32 days", period="10 days"
      )
      df_cv2 = diagnostics.cross_validation(
          m, horizon="32 days", period="10 days", initial="96 days"
      )
      assert ((df_cv1["y"] - df_cv2["y"]) ** 2).sum() == pytest.approx(
          0.0
      )
      assert (
          (df_cv1["yhat"] - df_cv2["yhat"]) ** 2
      ).sum() == pytest.approx(0.0)
  
imports: import datetime
  import itertools
  import numpy
  import pandas
  import pytest
  from prophet import Prophet, diagnostics
label_desc: Use image node_id 7 for calling the TestCrossValidation obj's underlying member method code with example usage: obj.test_cross_validation_default_value_check(ts_short, backend) without return types