Structural Break Phillips-Perron Unit Root Test
Also known as: break-augmented PP test, Phillips-Perron test with structural break, structural break unit root test, PP unit root test with break
The structural break Phillips-Perron (PP) unit root test extends the classical PP framework to allow for one or more discrete shifts in the level or trend of a time series. By endogenously or exogenously identifying break dates and controlling for them, it tests the null of a unit root against a trend-stationary alternative that accommodates structural change, avoiding the spurious acceptance of non-stationarity caused by ignored breaks.
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When to use it
Use this test when visual inspection or prior knowledge suggests that a macroeconomic or financial series may have experienced a structural break — such as a policy change, financial crisis, or regime shift — and you want to determine whether it is truly integrated or stationary around a broken trend. It is especially valuable when the standard PP or ADF test fails to reject the unit-root null and you suspect a missed break is distorting the result. Do not apply it when the series shows multiple frequent breaks (use the Lee-Strazicich or Lumsdaine-Papell test instead), when the break date is purely data-driven with no substantive justification (risk of spurious precision), or when the sample is very short (fewer than 60 observations), as critical values become unreliable.
Strengths & limitations
- Corrects the well-known size distortion of standard PP and ADF tests in the presence of structural breaks, which otherwise over-accept the unit-root null.
- Non-parametric long-run variance correction handles heteroscedasticity and serial correlation without requiring a specific lag selection criterion.
- Accommodates both exogenously specified and endogenously determined break dates, offering flexibility for theory-driven or data-driven applications.
- Produces break-point estimates alongside the unit-root test result, providing additional information about the timing and nature of structural change.
- Works with a single test regression rather than iterative lag augmentation, making computation straightforward.
- Designed for a single break; performance deteriorates when multiple structural breaks are present, requiring specialist multi-break tests.
- Endogenous break-date selection can overfit in small samples, and critical values depend on the location of the break in the sample.
- The non-parametric bandwidth (kernel) choice for the long-run variance correction can influence finite-sample size and power.
- Asymptotic critical values differ across break-model specifications (break in intercept, trend, or both), requiring careful matching of model to critical value table.
- Power against near-unit-root alternatives remains limited, as with all unit-root tests.
Frequently asked
How is the structural break PP test different from the Zivot-Andrews test?
Both extend standard unit-root tests to accommodate a single endogenous break, but Zivot and Andrews (1992) augment the Dickey-Fuller regression with lags, while Perron's structural break PP variant uses the nonparametric Phillips-Perron correction for serial correlation instead of lag augmentation. The choice between them often hinges on sample size and whether lag selection is a concern.
What if I suspect more than one structural break?
Single-break tests like the structural break PP test have low power when multiple breaks are present and can still fail to reject the unit-root null. Use the Lumsdaine-Papell (1997) two-break test or the Lee-Strazicich (2003) LM test, which allow for two endogenous breaks simultaneously.
Do I need to specify the break date before running the test?
Not necessarily. Perron (1997) provides an endogenous procedure that selects the break date by minimising the t-statistic on the lagged level, but you must then use the corresponding asymptotic critical values that account for this search procedure. If economic theory points to a known date, exogenous specification is simpler and uses different critical values.
How does the nonparametric PP correction work in this context?
After estimating the break-augmented regression by OLS, the residuals are used to compute the Newey-West long-run variance. This estimate adjusts the autoregressive coefficient and its t-statistic to account for autocorrelation and heteroscedasticity without adding AR lags, unlike the ADF approach. The bandwidth for the kernel estimator is typically chosen by an automatic rule such as Andrews (1991).
Can I use this test if my series has a known break such as COVID-19?
Yes. When a break date is well-motivated by an external event such as a financial crisis or a pandemic, specifying it exogenously is straightforward and uses simpler critical values. The test will then assess whether the series is stationary around that exogenously defined shift, which is the most defensible approach in such cases.
Sources
- Perron, P. (1997). Further evidence on breaking trend functions in macroeconomic variables. Journal of Econometrics, 80(2), 355-385. DOI: 10.1016/S0304-4076(97)00049-3 ↗
- 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 ↗
How to cite this page
ScholarGate. (2026, June 3). Structural Break Phillips-Perron Unit Root Test. ScholarGate. https://scholargate.app/en/econometrics/structural-break-pp-unit-root-test