Time series analysis using Prophet in Python — Part 1: Math explained

Time series analysis using Prophet in Python — Part 2: hyperparameter tuning and cross validation

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…