A1054
Title: Asymptotic and bootstrap inference for change-points in time series
Authors: Xinyi Tang - The Hang Seng University of Hong Kong (Hong Kong) [presenting]
Abstract: The asymptotic distribution of a change-point estimator is studied for piecewise stationary time series under various break sizes. In particular, the break sizes $\|\boldsymbol{d}_n\|=O(1/n^{\alpha})$ is considered for $0<\alpha<1/2$, $\alpha=1/2$ and $\alpha>1/2$, which represent large, moderate and small break sizes respectively, where $n$ is the sample size. It is shown that the asymptotic distributions in all three cases are different but are related to the maximizer of a two-sided drifted Brownian motion. Also, the distribution is pivotal for the cases $\alpha=1/2$ and $\alpha>1/2$, for which the analytical densities are derived for conducting statistical inference. In addition, a modified parametric bootstrap (MPB) and a modified block bootstrap (MBB) procedure are proposed to approximate the finite sample distribution of the change-point estimator, which are shown to work well under any break sizes. Extensive simulation studies are provided to demonstrate the promising performance of the proposed asymptotic and bootstrap distributions. Applications to financial time series are also illustrated.
