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...

Most of the asymptotic results for Markov regime-switching models with possible unit roots are based on specifications implying that the number of regime switches grows to infinity as the sample size increases. Conversely, in this note we derive some new asymptotic results for the case of Markov...

It is well known that the standard independent, identically distributed (iid) bootstrap of the mean is inconsistent in a location model with infinite variance (α-stable) innovations. This occurs because the bootstrap distribution of a normalised sum of infinite variance random variables tends...

In this note we discuss the properties of Augmented-Dickey-Fuller [ADF] unit root tests for autoregressive processes with a unit or near-unit root in the presence of multiple level shifts of large size. Due to the presence of level shifts, the ADF tests experience severe power losses. We...