Nonlinear PP Unit Root Test
Nonlinear Phillips-Perron Unit Root Test · Also known as: Nonlinear PP test, Nonlinear Phillips-Perron test, PP unit root test with nonlinear adjustment, nonlinear PP
The Nonlinear Phillips-Perron unit root test extends the classic PP test by allowing the adjustment toward equilibrium to follow a nonlinear path — such as a smooth transition or threshold mechanism — rather than assuming a constant linear speed of adjustment. This makes it more powerful when the true data-generating process involves regime-dependent or asymmetric mean-reversion dynamics.
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When to use it
Use the Nonlinear PP unit root test when you have strong theoretical or graphical reasons to believe that mean-reversion is regime-dependent — for example, exchange rates under managed float regimes, real interest differentials, or commodity prices subject to arbitrage thresholds. It outperforms the standard PP test when the true process involves smooth-transition or threshold stationarity and the error structure may be heteroscedastic or weakly dependent. Do not use it as a default replacement for the PP or ADF test: it requires specifying or estimating the transition function form, and its critical values differ from those of the linear PP test. Avoid it with very short series (fewer than 80 observations), as the nonlinear parameters are imprecisely estimated.
Strengths & limitations
- Higher power than the linear PP test when the true DGP exhibits threshold or smooth-transition mean-reversion.
- Retains the PP correction for serial correlation and heteroscedasticity, avoiding the need to select lag length.
- Suitable for economic time series with asymmetric adjustment dynamics, such as commodity prices or financial spreads.
- Does not impose a fixed linear adjustment speed, making it more flexible for real-world economic behavior.
- Requires choosing or estimating the form of the transition function (logistic, exponential), introducing specification uncertainty.
- Critical values differ from those of the linear PP test; simulated or bootstrapped critical values are needed.
- Suffers from low power in small samples (T < 80) because the nonlinear parameters are weakly identified under the unit-root null.
- Less widely implemented in standard statistical software than the linear PP test.
Frequently asked
How does the Nonlinear PP test differ from the KSS test?
The KSS test (Kapetanios, Shin, Snell 2003) uses an exponential smooth-transition specification and ADF-style lag augmentation to handle serial correlation. The nonlinear PP test applies the Phillips-Perron nonparametric correction instead of lag augmentation, so it does not require lag-length selection but the two approaches target similar nonlinear alternatives.
What transition function should I use?
The exponential STAR (ESTAR) specification is most common for symmetric adjustment (deviations in either direction trigger reversion), while the logistic STAR (LSTAR) is used for asymmetric adjustment. Choose based on economic theory about the nature of the adjustment process.
Can I use this test if my series has a structural break?
A structural break can mimic nonlinear behavior and inflate the test statistic. If a break is likely, prefer a test that allows for both a structural break and nonlinear adjustment, such as the nonlinear Zivot-Andrews test.
Do standard software packages implement this test?
Dedicated implementations are less common than for the linear PP test. R packages such as nls and custom code based on the KSS framework are typically used; specialized econometrics packages like EViews may offer similar nonlinear unit root routines.
What sample size is needed for reliable results?
At least 80 to 100 observations are advisable. With shorter series the nonlinear transition parameters are poorly identified under the null, reducing power and making inference unreliable.
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 ↗
- Kapetanios, G., Shin, Y., & Snell, A. (2003). Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics, 112(2), 359-379. DOI: 10.1016/S0304-4076(02)00202-6 ↗
How to cite this page
ScholarGate. (2026, June 3). Nonlinear Phillips-Perron Unit Root Test. ScholarGate. https://scholargate.app/en/econometrics/nonlinear-pp-unit-root-test
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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- Nonlinear ADF Unit Root TestEconometrics↔ compare
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- Nonlinear KPSS TestEconometrics↔ compare
- Phillips-Perron unit root testEconometrics↔ compare
- Zivot-Andrews Structural Break TestEconometrics↔ compare