How does the KPSS test differ from ADF in stationarity testing?

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AcadiFi · Accepted Answer

The KPSS (Kwiatkowski-Phillips-Schmidt-Shin) test reverses the null hypothesis of ADF: null is stationarity, alternative is unit root. This flip matters because unit-root tests generally have low power—ADF failing to reject could mean either a true unit root or insufficient data to detect stationarity. Running both tests provides confirmatory evidence: if ADF rejects unit root AND KPSS fails to reject stationarity, conclude the series is stationary with confidence.

KPSS regresses the series on a constant (and optionally trend), then computes a test statistic based on partial sums of residuals divided by a long-run variance estimator. Critical values at 5% are roughly 0.463 (level stationarity) or 0.146 (trend stationarity). If statistic exceeds critical value, reject stationarity.

Four possible outcomes arise from combining ADF and KPSS:
1. ADF rejects, KPSS fails to reject: series is stationary.
2. ADF fails to reject, KPSS rejects: series has unit root.
3. Both reject: inconclusive or regime change—check for structural breaks.
4. Neither rejects: insufficient data—gather more or accept uncertainty.

Long-run variance bandwidth selection affects KPSS. The Newey-West estimator with data-dependent bandwidth is standard. Finite sample performance suffers with small samples or persistent but stationary series (near-unit-root), making confirmatory testing the robust practice.

How does the KPSS test differ from ADF in stationarity testing?

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