The math behind Prophet
In Chapter 1, The History and Development of Time Series Forecasting, we introduced Prophet as an additive regression model. Figures 1.4 and 1.5 in that chapter illustrated this by showing how several different curves representing model components can simply be added together to arrive at a final model. Mathematically, this is represented with the following equation:
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(1) |
The model’s forecasted 
value at time 
is given by the 
function. This function consists of four components, summed together (or multiplied together; see Chapter 5, Working with Seasonality, for more on this):
is the growth component, or the general trend, which is non-periodic
is the seasonality component – that is, the summation of all periodic components
is the holiday component, representing all one-off special events
is the error term
