Monitoring multivariate time series

We derive online-monitoring cumulative sum (CUSUM) procedures for change points in multivariate time series. These procedures rely on recent advances in sharp multivariate strong invariance principles. Theoretical results show gains in power and shorter detection times to result from monitoring a multivariate time series instead of just one of its components. To sidestep the issue of estimating long-run covariance matrices, we employ a ratio-type detector. Using this approach, simulations show that the theoretical (asymptotic) advantages also show up in finite samples. An empirical application to S&P 500 log-returns shows that the faster detection can also be economically significant.