Foundations✓ Mathematical
◆ The PatternSeparating signal from noise, season from trend
Decomposition splits a time series into three components: trend (long-term direction), seasonality (repeating patterns), and residual (noise). This reveals the structure hidden in raw data and guides model choice.
yt = Tt + St + Rt (additive) | yt = Tt × St × Rt (multiplicative)
Additive when seasonal amplitude is constant. Multiplicative when it grows with the level.
// Interactive — STL decomposition
Seasonal Period12
Trend Strength50
# Python — STL decomposition from statsmodels.tsa.seasonal import STL stl = STL(series, period=12, robust=True) result = stl.fit() result.plot() # result.trend, result.seasonal, result.resid
Pattern bridge: Decomposition mirrors eigendecomposition in linear algebra — both break a complex object into orthogonal components. In markets, separating trend from noise is the trader’s version of the same problem.