Prophet

Prophet is a procedure for forecasting time series data based on an additive model where non-linear trends are fit with yearly, weekly, and daily seasonality, plus holiday effects. It works best with time series that have strong seasonal effects and several seasons of historical data. Prophet is robust to missing data and shifts in the trend, and typically handles outliers well.

Univariate, time series models

The Prophet model was developed by Facebook (now Meta) in 2018. It can be described as a non-linear regression model which can be written on the form

where g(t) describes the linear trend, s(t) describes various seasonal patterns and h(t) incorporates holiday effects. The final term εtεt is the error term which is not described by the model.

The linear trend is enhanced by introducing changepoints at specific points in the series, allowing it to be piecewise linear. This is useful for series when the trend can be approximated by a number of linear segments.

The seasonal part creates multiple seasonal patterns at various frequencies, making it possible to capture patterns at for example quarterly and monthly frequencies, along with an overall yearly seasonal pattern.

Finally, the holiday effects use dummy variables to model the effect different holidays may have on the data.

Fitting the model to data as well as selecting the number of changepoints, seasonal patterns and holiday effects is done automatically within a Bayesian framework.

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Prophet

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