STL Decomposition

When trend and seasonal patterns in a time series are messy or evolving, we use STL to extract them.

Trends may change gradually, and seasonal behaviours can vary year to year. This is why we need a more adaptable approach than classical decomposition.

from statsmodels.tsa.seasonal import STL

Seasonal-Trend decomposition using LOESS

• Unlike classical decomposition, STL allows seasonal patterns to change gradually.
• Better suited for real-world, non-stationary data.
• Produces adaptive seasonality and cleaner residuals compared to classical methods.
• Useful when you want to deseasonalize but the seasonality is not straightforward.

Key ideas:

• STL identifies one-off events (e.g., COVID dip) as irregular, not trend or seasonality.
• LOESS (Locally Estimated Scatterplot Smoothing) underpins STL, refining trend and seasonal estimates iteratively.
• Initial estimates use moving averages (trend via 12-month MA, seasonality via grouped monthly averages).
• Refinement ensures the seasonal component is centered (mean = 0 per cycle), preventing contamination of the trend.

Takeaway: STL is more flexible and robust than classical decomposition, making it a preferred choice when patterns evolve over time.

Related:

• Decomposition in Time Series

Resources:

• https://towardsdatascience.com/time-series-forecasting-made-simple-part-3-1-stl-decomposition-understanding-initial-trend-and-seasonality-prior-to-loess-smoothing/

Classical

With STL