Nonlinear Zivot-Andrews Unit Root Test
Also known as: NZA test, nonlinear structural break unit root test, Zivot-Andrews test with nonlinear adjustment, smooth transition Zivot-Andrews test
The Nonlinear Zivot-Andrews test extends the classical Zivot-Andrews structural-break unit root test by embedding smooth-transition nonlinear adjustment into the test regression. It jointly searches for an endogenous structural break and allows the speed of mean-reversion to vary with distance from the attractor, producing more power against nonlinear stationary alternatives than either test alone.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use the Nonlinear Zivot-Andrews test when you suspect a univariate time series may be stationary but with both a structural break at an unknown date and nonlinear reversion dynamics — common in energy prices, exchange rates, inflation, and environmental series. It is preferable to the linear Zivot-Andrews test when prior theory or a RESET-type test suggests nonlinear dynamics, and preferable to the KSS test when a level or trend shift is also plausible. Do not use it as a first-pass screening tool on all series; the gain in power comes with a need for careful choice of break type (intercept, trend, or both) and transition function. It is not suited to short series (fewer than about 80 observations) where simulation-based critical values become unreliable.
Strengths & limitations
- Higher power than the linear Zivot-Andrews test when adjustment is genuinely nonlinear.
- Higher power than the KSS test when a structural break accompanies the nonlinear dynamics.
- Endogenous break selection removes the need to pre-specify the break date.
- Accommodates the most common break types: intercept, trend, or both.
- Flexible ESTAR specification captures a broad class of nonlinear stationary alternatives.
- Requires a relatively large sample (at least ~80 observations) for reliable simulation-based critical values.
- The joint search over break dates and nonlinear parameters creates substantial computational burden.
- Assumes at most one structural break; two or more breaks require multi-break extensions.
- Interpretation is complicated when both the break type and transition function specification are uncertain.
Frequently asked
How does this test differ from the standard Zivot-Andrews test?
The standard Zivot-Andrews test assumes linear mean-reversion once a break is allowed. The nonlinear extension adds a smooth transition (ESTAR) component so the speed of reversion can vary with the size of the deviation from equilibrium. This gives higher power when adjustment is genuinely nonlinear.
How does it differ from the KSS test?
The KSS test allows for nonlinear (ESTAR) adjustment but assumes no structural break. The Nonlinear Zivot-Andrews test adds an endogenous break search, making it more powerful when both nonlinearity and a level or trend shift are present.
Which critical values should I use?
Model-specific critical values obtained by Monte Carlo simulation or bootstrap, calibrated to the sample size, break type, and transition function. Standard Dickey-Fuller or original Zivot-Andrews tables are not valid here.
What is the minimum sample size?
A general guideline is at least 80 observations. Below this threshold the break-search procedure has too few candidate points and the simulated critical values can be severely distorted.
Can I use this test before running a nonlinear cointegration analysis?
Yes. Establishing the order of integration of individual series — including whether they are stationary around a broken trend with nonlinear adjustment — is a standard preliminary step before nonlinear cointegration tests such as the threshold or smooth-transition cointegration frameworks.
Sources
- Zivot, E., & Andrews, D. W. K. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business & Economic Statistics, 10(3), 251–270. DOI: 10.1080/07350015.1992.10509904 ↗
- 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 Zivot-Andrews Unit Root Test. ScholarGate. https://scholargate.app/en/econometrics/nonlinear-zivot-andrews-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.
- Lee-Strazicich TestEconometrics↔ compare
- Zivot-Andrews TestEconometrics↔ compare