Monitoring procedure for parameter change in causal time series

We propose a new sequential procedure to detect change in the parameters of a process X = ( X t ) t ∈ Z belonging to a large class of causal models (such as AR( ∞ ), ARCH( ∞ ), TARCH( ∞ ), or ARMA–GARCH processes). The procedure is based on a difference between the historical parameter estimator and the updated parameter estimator, where both these estimators are quasi-likelihood estimators. Unlike classical recursive fluctuation test, the updated estimator is computed without the historical observations. The asymptotic behavior of the test is studied and the consistency in power as well as an upper bound of the detection delay is obtained. Some simulation results are reported with comparisons to some other existing procedures exhibiting the accuracy of our new procedure. This procedure coupled with retrospective tests is applied to solve off-line multiple breaks detection in the daily closing values of the FTSE 100 stock index.