pwl_trend_forecaster = Prophet(
    daily_seasonality=False,
    weekly_seasonality=False,
    yearly_seasonality=False
)
forecaster = TransformedTargetForecaster(
    [
        ("detrend", Detrender(forecaster=pwl_trend_forecaster)),
        ("forecast", ARIMA() )  
    ]
)

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sktime.forecasting.base                import ForecastingHorizon
from sktime.forecasting.trend               import ProphetPiecewiseLinearTrendForecaster
from sktime.forecasting.model_selection     import temporal_train_test_split
from sktime.forecasting.fbprophet           import Prophet
from sktime.performance_metrics.forecasting import MeanSquaredError

def Randomwalk1D(n): 
   y = 0
   yposition = [0] 
   for i in range(n-1):
       step = np.random.uniform(0,1)
       if step < 0.5:  
           y += 1  
       if step > 0.5:   
           y += -1 
       yposition.append(y)
   return yposition

n = 1000
np.random.seed(42)
mse = MeanSquaredError(square_root=True)
all_mse_current = []
all_mse_suggestion = []

for prior_scale in np.logspace(-3,-1/3,num=10): #values within 0.001 and 0.46
    for i in range(500):
        y = pd.Series(
                    data=Randomwalk1D(n),
                    index=pd.date_range('2016-01-01',periods=n, freq='15min')
                    )
        y_train, y_test = temporal_train_test_split(y)
        fh = ForecastingHorizon(y.index, is_relative=False)
        current = ProphetPiecewiseLinearTrendForecaster(
                            changepoint_prior_scale=prior_scale
                            )
        suggestion = Prophet(
                            daily_seasonality=False,
                            weekly_seasonality=False,
                            yearly_seasonality=False,
                            changepoint_prior_scale=prior_scale
                            )
        
        y_pred_current  = current.fit(y).predict(fh)
        y_pred_suggestion  = suggestion.fit(y).predict(fh)        
        mse_current = mse(y,y_pred_current)
        mse_suggestion = mse(y,y_pred_suggestion)

        all_mse_current.append(mse_current)
        all_mse_suggestion.append(mse_suggestion)

total = len(np.array(all_mse_current))
current_wins = np.sum(np.array(all_mse_current)<np.array(all_mse_suggestion))
suggestion_wins = np.sum(np.array(all_mse_current)>np.array(all_mse_suggestion))
ties = np.sum(np.array(all_mse_current)==np.array(all_mse_suggestion))

print(f"Out of {total} runs: \nThe current implementation is more accurate in "+
      f"{current_wins} ({np.round_(current_wins/total*100,1)}%) cases.\n"+
      f"The suggested change is more accurate in {suggestion_wins}"+
      f"({np.round_(suggestion_wins/total*100,1)}%) cases.\n"+
      f"In {ties} ({np.round_(ties/total*100,1)}%) cases they return the same value.")