How is 'yhat' (prediction) calculated in the fbprophet library?

Question

I am using fbprophet for time-series predictions in Python and I am wondering how the yhat (prediction) column is calculated. I used the following code.

import quandl
import fbprophet

tesla = quandl.get('WIKI/TSLA')
tesla = tesla.reset_index()
tesla = tesla.rename(columns={'Date': 'ds', 'Adj. Close': 'y'})
tesla = tesla[['ds', 'y']]

prophet = fbprophet.Prophet()
prophet.fit(tesla)
future = prophet.make_future_dataframe(periods=365)
future = prophet.predict(future)

The future dataframe contains the following columns:

['ds', 'trend', 'trend_lower', 'trend_upper', 'yhat_lower', 'yhat_upper', 
'seasonal', 'seasonal_lower', 'seasonal_upper', 'seasonalities', 
'seasonalities_lower', 'seasonalities_upper', 'weekly', 'weekly_lower', 
'weekly_upper', 'yearly', 'yearly_lower', 'yearly_upper', 'yhat']

I understand yhat is the prediction, but is it a combination of trend, seasonal, seasonalities, weekly, yearly or something else?

I have tried combining the trend, seasonal, seasonalities, weekly, yearly columns to see if they equal the yhat column, but they do not:

future['combination'] = future['trend'] + future['seasonal'] + future['weekly'] + future['yearly'] + future['seasonalities']

print(future[['combination', 'yhat']].head())

   combination       yhat
0    57.071956  27.681139
1    55.840545  27.337270
2    53.741200  26.704090
3    51.874192  26.148355
4    47.827763  25.065950

I have been unable to find an answer in the documentation, but apologize if I have simply missed it.

Answer 1

I am a beginner of fbprophet but would like to share my guess. Even though I'm not sure it is correct, The following equation probably holds true in the default setting of prophet.

yhat = trend + seasonal

Hopefully, my answer will help you!

Answer 2

This seems to have changed now. Looking at Github code, yhat is calculated as below

yhat = (trend * (1 + multiplicative_terms) + additive_terms

A link to this calculation in the fbprophet source code is found

• here for Python
• here for R