What is STL decomposition?

Seasonal-Trend decomposition using Loess (STL) is a method of decomposing a time series into three main components:

• Trend — the long-term progression of the data.
• Seasonality — repeating cycles or patterns associated with periodic changes.
• Residual — noise or random fluctuations not explained by the trend and seasonality.

The method is based on Loess local regression, which allows flexible approximation of the trend and seasonality without strict assumptions about the data's shape. This is useful for analyzing and forecasting time series where it is important to separate seasonal effects from the overall trend.

An example of using STL in Python with the statsmodels library:

from statsmodels.tsa.seasonal import STL
import pandas as pd

# Assume there is a time series data
stl = STL(data, seasonal=13)
result = stl.fit()

trend = result.trend
seasonal = result.seasonal
residual = result.resid

Thus, STL decomposition helps understand the structure of a time series and improve forecast quality.