Change-point methods for multivariate time-series: paired vectorial observations

Abstract

We consider paired and two-sample break-detection procedures for vectorial observations and multivariate time series. The new methods involve L2-type criteria based on empirical characteristic functions and are easy to compute regardless of dimension. We obtain asymptotic results that allow for application of the methods to a wide range of settings involving on-line as well as retrospective circumstances with dependence between the two time series as well as with dependence within each series. In the ensuing Monte Carlo study the new detection methods are implemented by means of resampling procedures which are properly adapted to the type of data at hand, be it independent or paired, autoregressive or GARCH structured, medium or heavy-tailed. The new methods are also applied on a real dataset from the financial sector over a time period which includes the Brexit referendum