Patterns › Time series

Stationarity tests (ADF + KPSS)

Stationarity tests check whether a series has a unit root: augmented Dickey-Fuller (H₀: unit root) alongside KPSS level and trend variants (H₀: stationary), with a combined verdict.

What is Stationarity tests (ADF + KPSS)?

ADF tests the null of a unit root — rejecting supports stationarity. KPSS flips the burden: its null is stationarity (around a level or a deterministic trend) — rejecting argues against it. Running both gives a 2×2 verdict grid: agreement is strong evidence; both rejecting hints at structural breaks or near-integration.

The p-values are interpolated from critical-value tables and truncated to [0.01, 0.10].

When should I use Stationarity tests (ADF + KPSS)?

  • Before ARIMA modeling, to decide the differencing order d.
  • Any analysis assuming a stable mean/variance over time.

What data does it need?

One numeric series column (row order = time order).

What does it report?

ADF statistic/lag/p, KPSS level and trend statistics/p, and a plain-language verdict.

What does it assume?

  • Regularly spaced observations in time order.
  • No large structural breaks (both tests lose power).

How do I interpret the result?

Stationary verdict → model levels directly; non-stationary → difference the series (d = 1) and re-test.

See also

References

  • Kwiatkowski, Phillips, Schmidt & Shin (1992). Testing the null of stationarity. J Econometrics 54.