To Örebro University

In this paper a new technique for monitoring shifts in covariance matrices of Gaussian processes is developed. The processes we monitor are obtained from the covariance matrices estimated using a single observation. These processes follow independent Gaussian distribution in the in-control state, thus allowing for application of standard control charts. Furthermore, in contrary to the existing literature, the suggested procedure is asymptotically robust to the shifts in the mean. The explicit out-of-control distribution for an arbitrary moment of the shift is derived. The performance of numerous multivariate control charts is evaluated in an extensive simulation study and applied to monitoring volatilities on financial markets.