Unit root test

In statistics, a unit root test tests whether a time series variable is non-stationary using an autoregressive model. A commonly used test that is valid in large samples is the augmented Dickey–Fuller test. The optimal finite sample tests for a unit root in autoregressive models were developed by Denis Sargan and Alok Bhargava by extending the work by John von Neumann, and James Durbin and Geoffrey Watson. In the observed time series cases, for example, Sargan-Bhargava statistics test the unit root null hypothesis in first order autoregressive models against one-sided alternatives, i.e., if the process is stationary or explosive under the alternative hypothesis. Another test is the Phillips–Perron test.

See also

• Augmented Dickey–Fuller test
• Dickey–Fuller test
• Phillips–Perron test
• KPSS test
• Zivot–Andrews test
• ADF-GLS test

References

• Bhargava, A. (1986). "On the Theory of Testing for Unit Roots in Observed Time Series". The Review of Economic Studies 53 (3): 369–384. doi:10.2307/2297634. JSTOR 2297634.
• Bierens, H.J. (2001). "Unit Roots," Ch. 29 in A Companion to Econometric Theory, editor B. Baltagi, Oxford: Blackwell Publishers, 610–633. "2007 revision"
• Dickey, D. A.; Fuller, W. A. (1979). "Distribution of the Estimators for Autoregressive Time Series with a Unit Root". Journal of the American Statistical Association 74 (366a): 427–431. doi:10.1080/01621459.1979.10482531.
• Enders, Walter (2004). Applied Econometric Time Series (Second ed.). John Wiley & Sons. pp. 170–175. ISBN 0-471-23065-0.
• Patterson, K. (2011), Unit Root Tests in Time Series 1, Palgrave Macmillan.
• Patterson, K. (2012), Unit Root Tests in Time Series 2, Palgrave Macmillan.
• Sargan, J. D.; Bhargava, Alok (1983). "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk". Econometrica 51 (1): 153–174. JSTOR 1912252.