Time series analysis using Prophet in Python — Part 1: Math explained
Published in
4 min readJul 8, 2020
Check out the video version here:
Prophet models time series as a generalized additive model (GAM) combining the trend function, seasonality function, holiday effects, and an error term in one model:
- 𝑔(𝑡) : trend (non-periodic changes)
- 𝑠(𝑡): seasonality (periodic changes)
- ℎ(𝑡) : holiday effect
- 𝜖𝑡: error term, default prior 𝜖∼𝑁(0,0.5)
1. Trend model
Logistic trend model
The logistic trend model is based on the logistic growth model:
𝑔(𝑡)=𝐶/(1+exp(−𝑘(𝑡−𝑚))
C: carrying capacity
k: growth rate
m: offset parameter
Here is an example plotting g(t) with m=0 and t from 0 to 49. As we can see here, carrying capacity and growth rate may…