Sequentielle Überwachung von Finanzzeitreihen anhand von Residuenkarten

In this paper, the focus is on sequential analysis of financial time series. Mean and variance of time series are simultaneously monitored. Initially, conventional control charts, well-known tools of statistical process control, are combined with the previously introduced characteristic quantity. The considered characteristic quantity is a vector including the residuals of the fitted model and their squares. Further, the respective control procedures are calibrated via simulation. The effectiveness of control schemes is demonstrated in the empirical example, where the main German share price index is studied during the financial crisis from 2006 until 2008. The main purpose is the identification of structural changes in mean or variance using predictions based on linear regression with time series errors applied to the considered price index and the GARCH model applied to logarithmic returns. Structural breaks are visualized by signals of the considered residual charts. Therefore, fluctuations on the capital market during financial crises are illustrated. Copyright Springer-Verlag Berlin Heidelberg 2014