# Probability and Statistics Seminar

### Monitoring Non-Stationary Processes

In nearly all papers on statistical process control for time-dependent data it is assumed that the underlying process is stationary. However, in finance and economics we are often faced with situations where the process is close to non-stationarity or it is even non-stationary.

In this talk the target process is modeled by a multivariate state-space model which may be non-stationary. Our aim is to monitor its mean behavior. The likelihood ratio method, the sequential probability ratio test, and the Shiryaev-Roberts procedure are applied to derive control charts signaling a change from the supposed mean structure. These procedures depend on certain reference values which have to be chosen by the practitioner in advance. The corresponding generalized approaches are considered as well, and generalized control charts are determined for state-space processes. These schemes do not have further design parameters. In an extensive simulation study the behavior of the introduced schemes is compared with each other using various performance criteria as the average run length, the average delay, the probability of a successful detection, and the probability of a false detection.

### Literature

• Lazariv T. and Schmid W. (2018). Surveillance of non-stationary processes. AStA - Advances in Statistical Analysis, https://doi.org/10.1007/s10182-018-00330-4 .
• Lazariv T. and Schmid W. (2018). Challenges in monitoring non-stationary time series. In Frontiers in Statistical Process Control, Vol. 12, pp. 257-275. Berlin: Springer.

Joint work with Taras Lazariv (European University Viadrina, Department of Statistics, Germany).