This study delves into the development and application of sequential algorithms for detecting spontaneous changes, or anomalies, in the probabilistic characteristics of multivariate time series. The research is primarily motivated by the challenges associated with providing mathematical support for decision-making processes that depend on data from multi-channel monitoring of large systems. The focus is on the spatial-temporal dynamics of multidimensional time series measurements. Unlike conventional approaches, this study proposes innovative techniques for examining inter-channel connections. These techniques involve reducing the dimensionality of the data by representing data matrices in terms of their first singular basis and employing multiple regression in the projection space. The paper also demonstrates the practical application of the developed approach in analyzing the characteristics of turbulent flow, based on measurements of pressure deviation at different spatial locations. This research contributes significantly to the field by offering a novel approach to anomaly detection in multivariate time series data.