Change detection in parametric multivariate dynamic data streams using the ARMAX-GARCH model

Dynamic data detection is one of the main concerns in the statistical process control (SPC) field. Here we focus on monitoring parametric multivariate dynamic data streams using the ARMAX-GARCH model, which reflects both the influence of exogenous variables on the mean vector and the heterogeneity of the covariance matrix. A quasi maximum likelihood estimator is used to estimate the parameter vector of a dynamic process, and a top-r control scheme is proposed to monitor the parameters of multi-dimensional data streams. Finally, a real-data example of monitoring landslide illustrates the superiorities of the proposed scheme.