Abrupt change in mean using block bootstrap and avoiding variance estimation

• Published in: Computational statistics Vol. 33; no. 1; pp. 413 - 441
• Main Authors: Peštová, Barbora, Pešta, Michal
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2018; Springer Nature B.V
• Subjects: Bootstrap method; Computer simulation; Computing time; Economic Theory/Quantitative Economics/Mathematical Methods; Mathematics and Statistics; Maxima; Null hypothesis; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistical analysis; Statistical methods; Statistical tests; Statistics; Variance; Hypothesis testing; Change point; Robustness; Block bootstrap; Change in mean; Ratio type statistics
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-017-0785-4

We deal with sequences of weakly dependent observations that are naturally ordered in time. Their constant mean is possibly subject to change at most once at some unknown time point. The aim is to test whether such an unknown change has occurred or not. The change point methods presented here rely on ratio type test statistics based on maxima of the cumulative sums. These detection procedures for the abrupt change in mean are also robustified by considering a general score function. The main advantage of the proposed approach is that the variance of the observations neither has to be known nor estimated. The asymptotic distribution of the test statistic under the no change null hypothesis is derived. Moreover, we prove the consistency of the test under the alternatives. A block bootstrap method is developed in order to obtain better approximations for the test’s critical values. The validity of the bootstrap algorithm is shown. The results are illustrated through a simulation study, which demonstrates computational efficiency of the procedures. A practical application to real data is presented as well.