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

can be written as,

where,

• is the deterministic component (trend, seasonal component, etc.)

• is the stochastic component.

• 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

  1. this is valid in large samples.

  Phillips–Perron test

• KPSS test

  1. 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

• "2007 revision"