Monitoring Multivariate Time Series Based on Joint Characteristic Function

In this paper, we investigate the change point monitoring problem in multivariate time series. To quickly detect changes in the marginal distribution as well as the time-dependent structure, we propose a CUSUM type monitoring statistic based on the joint characteristic function. The asymptotic properties of the monitoring statistic under the null hypotheses and alternative hypotheses are investigated theoretically. Given the complexity of the asymptotic distribution under the null hypothesis, a multivariate stationary bootstrap method is employed to estimate the critical value of the test. Numerical simulations and a real life case study demonstrate the effectiveness of the proposed methodology.