Testing for unit roots in autoregressions with multiple level shifts
AbstractThe asymptotic distributions of Augmented-Dickey-Fuller (ADF) unit root tests for autoregressive processes with a unit or near-unit root are discussed in the presence of multiple stochastic level shifts of large size occurring independently in time. The distributions depend on a Brownian motion and a Poisson-type jump process. Due to the latter, tests based on standard critical values experience power losses increasing rapidly with the number and the magnitude of the shifts. A new approach to unit root testing is suggested which requires no knowledge of either the location or the number of level shifts, and which dispenses with the assumption of independent shift occurrence. It is proposed to remove possible shifts from a time series by weighting its increments according to how likely it is, with respect to an ad hoc postulated distribution, a shift to have occurred in each period. If the number of level shifts is bounded in probability, the limiting distributions of the proposed test statistics coincide with those of ADF statistics under standard conditions. A Monte Carlo experiment shows that, despite their generality, the new tests perform well in finite samples.
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Bibliographic InfoPaper provided by Department of Statistics, University of Bologna in its series Quaderni di Dipartimento with number 2.
Date of creation: 2006
Date of revision:
Unit roots; level shifts; compound Poisson process; random fixed point;
Other versions of this item:
- Cavaliere, Giuseppe & Georgiev, Iliyan, 2007. "Testing For Unit Roots In Autoregressions With Multiple Level Shifts," Econometric Theory, Cambridge University Press, vol. 23(06), pages 1162-1215, December.
- C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
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- Herwartz, H. & Siedenburg, F., 2008. "Homogenous panel unit root tests under cross sectional dependence: Finite sample modifications and the wild bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 137-150, September.
- Herwartz, Helmut & Siedenburg, Florian, 2009. "The effects of variance breaks on homogenous panel unit root tests," Economics Working Papers 2009,07, Christian-Albrechts-University of Kiel, Department of Economics.
- Georgiev, Iliyan, 2010. "Model-based asymptotic inference on the effect of infrequent large shocks on cointegrated variables," Journal of Econometrics, Elsevier, vol. 158(1), pages 37-50, September.
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