COVARIANCE MONITORING OF HIGH DIMENSIONAL TIME SERIES HEALTH DATA UNDER VIOLATION OF SELECTED ASSUMPTIONS

Abstract

Monitoring covariance structures in high-dimensional time series is crucial for understanding
evolving dependencies in complex systems such as healthcare, finance, and industrial processes.
Traditional covariance estimators often fail when the number of variables exceeds the sample
size or when data contain outliers, non-stationarity, and structural changes. This study examines
robust and sparse covariance estimation techniques for high-dimensional time series, with
application to healthcare data in Nigeria. A simulation study based on multivariate
autoregressive models was conducted under stationary and non-stationary conditions. Sample
sizes (n = 100, 300), dimensions (p = 10, 15, 150), contamination levels (0%, 5%, 10%), and
mean shifts were considered. Data were generated from normal and heavy-tailed distributions.
Performance was evaluated using Mean Squared Error, Frobenius Norm Error, Condition
Number, and change-detection metrics. Three estimators were compared: Minimum Covariance
Determinant (MCD), Ridge, and Graphical LASSO, with covariance changes detected using the
CUSUM procedure. Results show that MCD consistently provides superior robustness across
contamination levels and dimensions. Ridge and LASSO perform well under clean normal data
but deteriorate with outliers and structural shifts, especially in small samples. Robust covariance
estimation, particularly MCD, offers a reliable framework for monitoring high-dimensional
healthcare time series.