A General Procedure for Change-Point Detection in Multivariate Time Series

We consider the change-point detection in a general class of time series models, including multivariate continuous and integer- valued time series. We propose a Wald-type statistic based on the estimator performed by a general contrast function, which can be constructed from the likelihood, a quasi-likelihood, a least squares method, etc. Sufficient conditions are provided to ensure that the test statistic convergences to a well-known distribution under the null hypothesis (of no change) and diverges to infinity under the alternative, which establishes the consistency of the procedure. Some examples of models are detailed to illustrate the scope of application of the proposed change-point detection tool. The procedure is applied to simulated and real data examples for numerical illustration.