Unit root test

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

• "2007 revision"

References

1. (2014). "Elements of Time Series Econometrics: An Applied Approach". [[Karolinum Press]].
2. (1979). "Distribution of the estimators for autoregressive time series with a unit root". [[Journal of the American Statistical Association]].