Modified Block Bootstrap Testing for Persistence Change in Infinite Variance Observations

Abstract

This paper investigates the properties of the change in persistence detection for observations with infinite variance. The innovations are assumed to be in the domain of attraction of a stable law with index κ∈(0,2]. We provide a new test statistic and show that its asymptotic distribution under the null hypothesis of non-stationary I(1) series is a functional of a stable process. When the change point in persistence is not known, the consistency is always given under the alternative, either from stationary I(0) to non-stationary I(1) or vice versa. The proposed tests can be used to identify the direction of change and do not over-reject against constant I(0) series, even in relatively small samples. Furthermore, we also consider the change point estimator which is consistent and the asymptotic behavior of the test statistic in the case of near-integrated time series. A block bootstrap method is suggested to determine critical values because the null asymptotic distribution contains the unknown tail index, which results in critical values depending on it. The simulation study demonstrates that the block bootstrap-based test is robust against change in persistence for heavy-tailed series with infinite variance. Finally, we apply our methods to the two series of the US inflation rate and USD/CNY exchange rate, and find significant evidence for persistence changes, respectively, from I(0) to I(1) and from I(1) to I(0).