In recent years, matrix-valued data has received an increasing amount of attention. This is due to their frequent application in various fields, such as signal processing, finance, medicine, engineering, among others. Here we consider matrix-valued time series processes and our aim is to detect changes in the mean behavior.
An obvious way to handle the problem is to make use of vectorization, i.e. the columns of the matrix are written together as a matrix. The problem is then reduced to the detection of a change in a vector time series. Such problems have been discussed by, e.g. Kramer and Schmid (1997), Bodnar et al. (2023), and Bodnar et al. (2024). The disadvantage of vectorization consists in the fact that the resulting time series process may be high-dimensional and the process identification is quite difficult.
In the last five years, other types of matrix-valued time series processes have been proposed (e.g., Chen et al. (2021), Wu and Bi (2023)). These approaches are characterized by fewer parameters and, for that reason, are of great interest in practice.
Using these new types of time series model, EWMA control charts for matrix-valued time series are derived. The control design is calculated, and some explicit results are given for matrix-valued autoregressive processes. The performance of the charts is compared with each other within an extensive simulation study.

Joint work with:
- S. Knoth, Department of Economics and Social Sciences, Institute of Mathematics and Statistics, Helmut Schmidt University, Hamburg, Germany
- Y. Okhrin, Department of Statistics and Data Science, Faculty of Business and Economics, University of Augsburg, Germany
- V. Petruk, Department of Statistics, Faculty of Business Administration and Economics, European University Viadrina, Frankfurt (Oder), Germany