Testing for unit roots in autoregressions with multiple level shifts

Cavaliere, Giuseppe ; Georgiev, Iliyan (2006) Testing for unit roots in autoregressions with multiple level shifts. Bologna, IT: Dipartimento di Scienze Statistiche "Paolo Fortunati", Alma Mater Studiorum Università di Bologna, p. 99. DOI 10.6092/unibo/amsacta/2260. In: Quaderni di Dipartimento. Serie Ricerche ISSN 1973-9346.
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The 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.

Document type
Monograph (Working Paper)
Cavaliere, Giuseppe
Georgiev, Iliyan
Unit roots, level shifts, compound Poisson process, random fixed point
Deposit date
26 Oct 2006
Last modified
16 May 2011 12:04

Other metadata

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