Phillips-Perron (PP) Unit-Root Test
Also known as: PP test, Phillips-Perron unit root test, Phillips-Perron birim kök testi
The Phillips-Perron test, proposed by Peter Phillips and Pierre Perron in 1988, tests for a unit root in a time series, like the Augmented Dickey-Fuller test, but corrects for autocorrelation and heteroskedasticity in the errors non-parametrically rather than by adding lagged differences. It runs a simple Dickey-Fuller regression and then adjusts the test statistic using a long-run variance estimate, so the practitioner need not choose a lag length for the regression itself.
Key highlights
- Requires no choice of lag length in the test regression, sidestepping a sensitive ADF tuning decision.
- Robust to general forms of autocorrelation and heteroskedasticity in the errors via the long-run variance correction.
- Shares ADF's hypotheses and critical values, so it slots directly into the same workflow as a robustness check.
- Widely implemented and reported alongside ADF in applied time-series studies.
Intuition
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How it works
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When to use it
Use the Phillips-Perron test as an alternative or complement to ADF when checking a series for a unit root, particularly when you are unsure how to specify the lag length or when the errors may be heteroskedastic. Because it shares ADF's hypotheses and critical values but handles short-run dynamics through a long-run variance estimate, the two often appear together in applied work as a robustness check. It assumes the long-run variance is well estimated, which requires choosing a bandwidth (lag truncation) for the Newey-West correction. Like ADF, it has low power against persistent stationary alternatives and can be distorted by negative moving-average errors or structural breaks, so it is best paired with the complementary KPSS test.
Strengths & limitations
- Requires no choice of lag length in the test regression, sidestepping a sensitive ADF tuning decision.
- Robust to general forms of autocorrelation and heteroskedasticity in the errors via the long-run variance correction.
- Shares ADF's hypotheses and critical values, so it slots directly into the same workflow as a robustness check.
- Widely implemented and reported alongside ADF in applied time-series studies.
- Still has low power against highly persistent (near-unit-root) stationary series, like all unit-root tests.
- Performs poorly when the errors contain a large negative moving-average component, over-rejecting the null.
- Requires a bandwidth choice for the long-run variance, to which results can be sensitive.
- Vulnerable to structural breaks, which can be mistaken for a unit root.
Common pitfalls
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Applications
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Frequently asked
How does Phillips-Perron differ from ADF?
Both test the same unit-root null with the same critical values. ADF removes serial correlation by adding lagged differences to the regression; Phillips-Perron keeps the regression simple and corrects the statistic afterwards using a heteroskedasticity- and autocorrelation-consistent long-run variance. ADF requires a lag choice; PP requires a bandwidth choice.
Which should I trust if ADF and PP disagree?
Disagreement usually signals borderline persistence or misspecification. Examine the error structure: PP is known to over-reject when there is a strong negative moving-average component, while ADF can be sensitive to lag choice. Running the complementary KPSS test, whose null is stationarity, helps adjudicate.
Does PP need a lag length?
Not for the regression, but it does require a bandwidth (lag truncation) for estimating the long-run variance in the correction term. Results can be sensitive to this choice, so it should be reported.
Sources
- 1.Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346.
- 2.Newey, W. K., & West, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 55(3), 703–708.
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Cite this page
ScholarGate. (2026, June 2). Phillips-Perron Test. ScholarGate. https://scholargate.app/econometrics/phillips-perron-test