Bootstrapping confidence intervals for the change-point of time series

Details Bootstrapping confidence intervals for the change-point of time series Bootstrapping confidence intervals for the change-point of time series

2007-06-11

arxiv.org/abs/0706.1485v1

Journal of Time Series Analysis. 29:947-972, 2008

Mathematics

Statistics Theory

25 pages, 25 figures

Scientific paper

10.1111/j.1467-9892.2008.00589.x

We study an AMOC time series model with an abrupt change in the mean and dependent errors that fulfill certain mixing conditions. We obtain confidence intervals for the unknown change-point via bootstrapping methods. Precisely we use a block bootstrap of the estimated centered error sequence. Then we reconstruct a sequence with a change in the mean using the same estimators as before. The difference between the change-point estimator of the resampled sequence and the one for the original sequence can be use as an approximation of the difference between the real change-point and its estimator. This enables us to construct confidence intervals using the empirical distribution of the resampled time series. A simulation study shows that the resampled confidence intervals are usually closer to their target levels and at the same time smaller than the asymptotic intervals.

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