Abstract

We deal with a situation such that some phenomena can cause several related events and each event contributes to a different univariate counting process. A collection of these naturally dependent point processes therefore forms a flexible multivariate counting process, where neither stationarity nor independence of interarrival times of the marginal processes are assumed. Our main aim is to detect a structural break of the event's occurrences over time, which means to test whether some (not necessarily all) intensities of the univariate counting processes are subject to change at some unknown time point. We investigate the asymptotic behavior of the test statistic under the null hypothesis as well as under the alternatives. The proposed band bootstrap overcomes the computational curse of dimensionality, while it preserves the dependencies within and between the processes. The validity of this novel resampling technique is proved. As a by-product, a changepoint estimator is introduced and its consistency is provided. Multiple changepoints' detections are designed. The empirical properties are illustrated in a simulation study. The unsupervised data-driven detection procedure is presented through an actuarial problem concerning claims from various insurance lines of business.