difficulty 3/5
Stationarity
The assumption that a series' mean, variance and correlation structure do not change over time. Nearly every time-series method needs it, and ordinary regression fails loudly without it.
Intuition
Take two quantities that have nothing to do with each other, measure both monthly for twenty years, and plot them on the same axes. Often they will look like the same line. Fit a regression and it will report a strong relationship with a tiny p-value.
The usual explanation offered is "correlation is not causation", which is true but beside the point, because here there is no correlation to explain. In the worked example below the two series are independent by construction — there is nothing at all to find — and the test still rejects its null 84% of the time.
The reason is that both series wander. A test built for data whose mean stays put is being handed data whose mean does not, and it has no way to notice [2, §12.3]. Stationarity is the property that makes the rest of time-series analysis legal, and checking for it is the first thing to do with any series [1, §6.4.4.2].
Formal definition
How it works
Where it's used
Why & when
Worked example
Pitfalls
Check yourself
3 questions
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Sources
- NIST/SEMATECH e-Handbook of Statistical Methodsstandard · retrieved 2026-09-13https://www.itl.nist.gov/div898/handbook/pmc/section4/pmc442.htm
- Think Stats, 2nd ed.book · retrieved 2026-09-13https://greenteapress.com/thinkstats2/html/index.html
- e-Handbook of Statistical Methods — 6.4.4.6 Box-Jenkins Model Identificationstandard · retrieved 2026-10-04https://www.itl.nist.gov/div898/handbook/pmc/section4/pmc446.htm