Testing for unit roots in autoregressions with multiple level shifts

Giuseppe Cavaliere, Iliyan Georgiev

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)1162-1215
JournalEconometric Theory
Volume23
Issue number6
DOIs
Publication statusPublished - 1 Jan 2007

Keywords

  • INFREQUENT PERMANENT SHOCKS
  • OIL-PRICE SHOCK
  • TIME-SERIES
  • UNKNOWN TIME
  • ALTERNATIVE HYPOTHESIS
  • STOCHASTIC INTEGRALS
  • STRUCTURAL BREAKS
  • TREND BREAKS
  • GREAT CRASH
  • COINTEGRATION

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