Unit root test
Time series statistical test
title: "Unit root test" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["time-series-statistical-tests"] description: "Time series statistical test" topic_path: "general/time-series-statistical-tests" source: "https://en.wikipedia.org/wiki/Unit_root_test" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::summary Time series statistical test ::
In statistics, a unit root test tests whether a time series variable is non-stationary and possesses a unit root. The null hypothesis is generally defined as the presence of a unit root and the alternative hypothesis is either stationarity, trend stationarity or explosive root depending on the test used.
General approach
In general, the approach to unit root testing implicitly assumes that the time series to be tested [y_t]_{t=1}^T can be written as,
:y_t = D_t + z_t + \varepsilon_t
where,
-
D_t
is the deterministic component (trend, seasonal component, etc.)
-
z_t is the stochastic component.
-
\varepsilon_t is the stationary error process. The task of the test is to determine whether the stochastic component contains a unit root or is stationary.
Main tests
Other popular tests include:
- augmented Dickey–Fuller test
- : this is valid in large samples.
- Phillips–Perron test
- KPSS test
- : here the null hypothesis is trend stationarity rather than the presence of a unit root.
- ADF-GLS test Unit root tests are closely linked to serial correlation tests. However, while all processes with a unit root will exhibit serial correlation, not all serially correlated time series will have a unit root. Popular serial correlation tests include:
- Breusch–Godfrey test
- Ljung–Box test
- Durbin–Watson test
Notes
References
References
- (2014). "Elements of Time Series Econometrics: An Applied Approach". [[Karolinum Press]].
- (1979). "Distribution of the estimators for autoregressive time series with a unit root". [[Journal of the American Statistical Association]].
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