Breaking a series apart
A time series is easier to understand when split into parts. Decomposition separates it into a long term trend, a repeating seasonal cycle, and a remaining residual.
The three components
- Trend is the slow direction of the series, rising or falling over time.
- Seasonality is a pattern that repeats over a fixed period, like weekly or yearly cycles.
- Residual is what remains after removing trend and seasonality, ideally just noise.
Additive versus multiplicative
- An additive model adds the parts, fitting series whose swings stay roughly constant.
- A multiplicative model multiplies them, fitting series whose swings grow with the level.
- Taking a logarithm can turn a multiplicative pattern into an additive one.
Why decompose
- It reveals the underlying trend hidden under seasonal noise.
- It lets you deseasonalize data for fairer comparisons across periods.
- The residual is a good place to hunt for anomalies.
Key idea
Decomposition splits a series into trend, repeating seasonality, and residual noise, which clarifies patterns and exposes anomalies in the leftover signal.