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Prophet

#time-series

Gist

Facebook's lauded model for Time Series Analysis and forecasting

Definition

Published in

First, they use a decomposable time series model:

y(t)=g(t)+s(t)+h(t)+ϵt,

where g(t) is the trend function (non-periodic changes in the value of the time series), s(t) represents periodic changes such as weekly and yearly seasonality, and h(t represents the effects of holidays which occur on potentially irregular scheduels over one or more days. and ϵt represents any idiosyncratic changes which are not accompodated by the model.

Oh

The authors point out that this specification is similar to Generalized additive model (GAM)

Interestingly, the authors talk about how it’s a “curve-fitting exercise” and admits that you are giving up the important inferential advantages but the advantages you gain are:

  1. Flexibility - accomodate seasonality with multiple periods
  2. Measurments do not need to be regularly spaced (no need to interpolate missing values) unlike ARIMA
  3. Fitting very fast
  4. Easily interpretable parameters that can be changed by the analyst to imppose assumption
Works

Time series that have strong seasonality and several seasons of historical data

The Trend Model

The original paper had: a saturating growth model and a piecewise linear model

The authors point out how modeling growth at facebook is similar to population growth in a natural ecosystems. And they cite the Hutchinson 1978 paper about logistic growth with a carrying capacity. Lol, I wonder if Mark Zuckerburg would be like “I don’t believe in carrying capacity, infinite growth—let me show you the Metaverse.”

In the growth model, they suggest that the carrying capacity is not constant as people will have access to the internet so they replace the carrying capacity (I despise how they used C instead of K) with C(t). Also the growth rate is not constant.

They added Changepoints

But they also have a simpler linear-trend with changepoints.