Unit-root and stationarity tests
Decide what kind of persistence a series supports
Unit-root diagnostics distinguish persistent stochastic trends from stationarity around a level or deterministic trend. ADF includes lagged differences to handle serial dependence; Phillips-Perron adjusts the test statistic using a long-run variance estimate. Both test a unit-root null. KPSS reverses the null to stationarity, making disagreement diagnostically useful rather than a voting contest.
Use before choosing levels, differences or cointegration models for time series. Specify plausible trends and breaks from the substantive setting, and ensure the observed history can distinguish slow mean reversion from non-stationarity.
Strengths
- Makes the stationarity assumption testable
- Complementary nulls reveal ambiguous evidence
Limitations
- Low power against highly persistent stationary alternatives
- Breaks and poor lag or bandwidth choices can distort conclusions
Know the boundary
A KPSS rejection means evidence against stationarity, while an ADF rejection means evidence against a unit root. Their p-values answer different questions.