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.
can be written as, where, The task of the test is to determine whether the stochastic component contains a unit root or is stationary.
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: