Unit root test

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==