Joint Detection of Structural Change and Nonstationarity in Autoregressions

Pitarakis, J (2011): Joint Detection of Structural Change and Nonstationarity in Autoregressions. Unpublished.

Abstract

In this paper we develop a test of the joint null hypothesis of parameter stability and a unit root within an ADF style autoregressive specification whose entire parameter structure is potentially subject to a structural break at an unknown time period. The maintained underlying null model is a linear autoregression with a unit root, stationary regressors and a constant term. As a byproduct we also obtain the limiting behaviour of a related Wald statistic designed to solely test the null of parameter stability in an environment with a unit root. These distributions are free of nuisance parameters and easily tabulated. The finite sample properties of our tests are subsequently assessed through a series of simulations.

• Item Type: MPRA Paper
• Language: English
• Keywords: Structural Breaks, Unit Roots, Nonlinear Dynamics
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C10 - General; C - Mathematical and Quantitative Methods > C2 - Econometric Methods: Single Equation Models; Single Variables > C22 - Time-Series Models; Dynamic Quantile Regressions

References

Andrews, D. W. K., (1993), `Tests for Parameter Instability and Structural Change with Unknown Change Point,' Econometrica, Vol. 61, pp. 821-856.

Bai, J. (1998), `A Note On Spurious Break,' Econometric Theory, Vol. 14, pp. 663-669.

Banerjee, A., R. L. Lumsdaine and Stock, J. H. (1992), `Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence,' Journal of Business & Economic Statistics, Vol. 10, pp 271-87.

Caner, M. and Hansen, B. E. (2001), `Threshold Autoregression with a Unit Root,' Econometrica, Vol. 69, pp. 1555-1596.

Hansen, B. E. (1997), `Approximate asymptotic p-values for structural change tests,' {\it Journal of Business and Economic Statistics}, Vol. 15, pp. 60-67.

Hamilton, J. D. (1994), Time Series Analysis, Princeton University Press.

Harris, D., Harvey, D. I., Leybourne, S. J. and Taylor, A. M. R. (2009), `Testing For A Unit Root In The Presence Of A Possible Break In Trend,' {\it Econometric Theory}, Vol. 25, pp. 1545-1588.

Kim, D. and Perron, P. (2009), `Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses,' {\it Journal of Econometrics}, Vol. 148, pp. 1-13.

Perron, P. (1989), `The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis,' {\it Econometrica,} Vol. 57, pp. 1361-1401.

Pitarakis, J. (2008), `Threshold Autoregressions with a unit root: Comment,' {\it Econometrica}, Vol. 76, pp. 1207-1217.

Zivot, E. and Andrews, D. W. K (1992), `Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis,' {\it Journal of Business & Economic Statistics, Vol. 10, pp. 251-70.