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Sequences of random objects arise from many real applications, including highthroughput omic data and functional imaging data. Those sequences are usuallydependent, non-linear, or even Non-Euclidean, and an important problem ischange-point detection in such dependent sequences in Banach spaces or metricspaces. The problem usually requires the accurate inference for not onlywhether changes might have occurred but also the locations of the changes whenthey did occur. To this end, we first introduce a Ball detection function andshow that it reaches its maximum at the change-point if a sequence has only onechange point. Furthermore, we propose a consistent estimator of Ball detectionfunction based on which we develop a hierarchical algorithm to detect allpossible change points. We prove that the estimated change-point locations areconsistent. Our procedure can estimate the number of change-points and detecttheir locations without assuming any particular types of change-points as achange can occur in a sequence in different ways. Extensive simulation studiesand analyses of two interesting real datasets wind direction and Bitcoin pricedemonstrate that our method has considerable advantages over existingcompetitors, especially when data are non-Euclidean or when there aredistributional changes in the variance.

Hierarchical Change-Point Detection for Multivariate Time Series via a Ball Detection Function