difficulty 2/5
Time series decomposition
Splitting a series into trend, a repeating seasonal pattern, and what is left. Three readable things in place of one unreadable one, and the basis of most forecasting methods.
Intuition
A single time series is usually asked three questions at once. Is it growing? Does it repeat? Is anything unusual happening? A plot of the raw numbers answers none of them well, because all three effects are superimposed and the largest one hides the rest.
Decomposition separates them. It rests on a modelling assumption that is close to universal in the field: "most time series analysis is based on the modeling assumption that the observed series is the sum of three components" — a trend, "a smooth function that captures persistent changes"; seasonality, "periodic variation, possibly including daily, weekly, monthly, or yearly cycles"; and noise, "random variation around the long-term trend" [1, §12.4].
Having them apart is what makes each one checkable. A trend you can extrapolate, a seasonal pattern you can plan staffing around, and a remainder you can test for whether anything is left in it.
Formal definition
How it works
Where it's used
Why & when
Worked example
Pitfalls
Check yourself
3 questions
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Sources
- Think Stats, 2nd ed.book · retrieved 2026-09-13https://greenteapress.com/thinkstats2/html/index.html
- Forecasting: theory and practice (2022)paperhttps://ar5iv.labs.arxiv.org/html/2012.03854
- NIST/SEMATECH e-Handbook of Statistical Methodsstandard · retrieved 2026-09-13https://www.itl.nist.gov/div898/handbook/pmc/section4/pmc444.htm