KPSS Stationarity Test
Also known as: Kwiatkowski-Phillips-Schmidt-Shin test, stationarity test, KPSS durağanlık testi
The KPSS test, introduced by Kwiatkowski, Phillips, Schmidt and Shin in 1992, tests the null hypothesis that a series is stationary against the alternative that it contains a unit root — the reverse of the ADF and Phillips-Perron tests. By flipping the burden of proof, it is designed to be used alongside unit-root tests so that the two can confirm one another and expose ambiguous, borderline cases.
Key highlights
- Reverses the null to stationarity, providing independent, confirmatory evidence to pair with ADF and PP.
- Directly targets the practically important question of whether a series can be treated as stationary.
- Robust long-run-variance scaling accommodates autocorrelation and heteroskedasticity in the errors.
- Standard component of the modern unit-root testing workflow, widely implemented.
Intuition
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How it works
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When to use it
Use KPSS together with ADF and Phillips-Perron when determining a series' order of integration. The recommended practice is confirmatory: if a unit-root test rejects its null and KPSS fails to reject stationarity, you have strong, consistent evidence of stationarity; the reverse pattern gives strong evidence of a unit root; agreement in the 'wrong' direction or rejection by both flags an ambiguous series (possibly fractionally integrated or subject to a structural break) that warrants closer study. KPSS requires a long-run-variance bandwidth and, like its counterparts, can be distorted by structural breaks. It is especially valuable precisely because unit-root tests have low power, so a stationarity-null test provides an independent line of evidence.
Strengths & limitations
- Reverses the null to stationarity, providing independent, confirmatory evidence to pair with ADF and PP.
- Directly targets the practically important question of whether a series can be treated as stationary.
- Robust long-run-variance scaling accommodates autocorrelation and heteroskedasticity in the errors.
- Standard component of the modern unit-root testing workflow, widely implemented.
- Results depend on the bandwidth chosen for the long-run variance, sometimes materially.
- Has limited power to distinguish a true unit root from a highly persistent stationary process.
- Sensitive to structural breaks, which can trigger spurious rejection of stationarity.
- Uses non-standard critical values that differ by deterministic specification, so the trend choice matters.
Common pitfalls
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Applications
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Frequently asked
Why use KPSS if I already ran ADF?
Because ADF has low power, failing to reject a unit root is weak evidence. KPSS reverses the null to stationarity, so running both lets them confirm one another: a clean conclusion is when one test rejects and the other does not, in mutually consistent directions.
What does it mean if both ADF and KPSS reject?
ADF rejecting a unit root while KPSS rejects stationarity is a contradictory signal. It often points to a series that is neither cleanly stationary nor a pure unit root — for example, a fractionally integrated process or one with a structural break — and calls for more careful modelling.
Is the KPSS test left- or right-tailed?
Right-tailed. The statistic grows when a random-walk component is present, so you reject the stationarity null for large values, using the non-standard critical values appropriate to whether a trend was included.
Sources
- 1.Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1–3), 159–178.
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ScholarGate. (2026, June 2). KPSS Test. ScholarGate. https://scholargate.app/econometrics/kpss-test