Phillips-Perron Unit Root Test
Also known as: PP test, PP unit root test, Phillips-Perron test, nonparametric unit root test
The Phillips-Perron (PP) test is a nonparametric unit root test for time series that corrects for serial correlation and heteroscedasticity in the error term without adding lagged differences. Introduced by Phillips and Perron (1988), it applies a kernel-based long-run variance estimator to adjust the Dickey-Fuller statistic, making it robust to a wide class of weakly dependent error processes.
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When to use it
Use the Phillips-Perron test when you need to assess whether a time series is integrated of order 1 (I(1)) before applying cointegration tests, VECM, or first-differencing. It is especially appropriate when errors may be serially correlated or heteroscedastic but you do not want to commit to a specific lag model — the PP test handles these features nonparametrically. It is preferred over the ADF when the sample is moderate-sized and serial correlation is suspected to follow a complex, unknown pattern. Do not use it when the time series is short (fewer than ~50 observations), as kernel corrections are unreliable in small samples. When a structural break is suspected, use the Zivot-Andrews test instead, because the PP test has low power in the presence of level shifts.
Strengths & limitations
- Robust to a wide class of serial correlation and heteroscedasticity without specifying a lag model.
- Avoids over-parameterization by not adding lagged differences, keeping degrees of freedom intact.
- Asymptotically equivalent to the ADF test, so critical values and interpretation are familiar.
- Handles both short-memory and weakly dependent errors through the nonparametric long-run variance correction.
- Available in virtually all major econometric software (R, Stata, EViews, Python).
- Low power in small samples (n < 50) because kernel-based long-run variance estimates are imprecise.
- Performs poorly when the data generating process contains a structural break — can falsely fail to reject the unit root null.
- The choice of bandwidth (truncation lag) affects the test statistic, and there is no universally optimal rule.
- Like all unit root tests, it has low power when the root is close to but strictly less than one (near-unit-root processes).
Frequently asked
What is the null hypothesis of the Phillips-Perron test?
The null hypothesis is that the time series contains a unit root (is non-stationary, integrated of order 1). Rejecting the null supports stationarity of the series.
How is the PP test different from the ADF test?
Both test the same null hypothesis and share the same asymptotic critical values. The ADF adds lagged differences to the regression to account for serial correlation (parametric), while the PP test corrects the test statistic using a nonparametric kernel estimator of the long-run variance. The PP test uses fewer degrees of freedom but is sensitive to bandwidth choice.
How do I choose the bandwidth for the PP test?
The most common practice is to use the Newey-West automatic bandwidth selector, which is the default in most software. This sets the truncation lag proportional to T^(1/4) or T^(2/9) depending on the kernel. Avoid manual selection unless you have a specific theoretical motivation.
What should I do if the PP test and ADF test give conflicting results?
Conflicting results are common and usually signal that the series is near-integrated. In such cases, also run the KPSS test (which has stationarity as the null) to triangulate. Consider whether a structural break might be driving the discrepancy and apply the Zivot-Andrews test.
Does the PP test work for seasonal data?
The standard PP test is not designed for seasonal unit roots. For seasonal time series, use a seasonal unit root test such as the HEGY test. The PP test can be applied after seasonal adjustment or first seasonal differencing.
Sources
- Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346. DOI: 10.1093/biomet/75.2.335 ↗
- Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press. ISBN: 978-0691042893
How to cite this page
ScholarGate. (2026, June 3). Phillips-Perron Unit Root Test. ScholarGate. https://scholargate.app/en/econometrics/phillips-perron-unit-root-test
Which method?
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