Robust filtering of time series with trends

Abstract

We develop and test a robust procedure for extracting an underlying signal in form of a time-varying trend from very noisy time series. The application we have in mind is online monitoring data measured in intensive care, where we find periods of relative constancy, slow monotonic trends, level shifts and many measurement artifacts. A method is needed which allows a fast and reliable denoising of the data and which distinguishes artifacts from clinically relevant changes in the patient's condition. We use robust regression functionals for local approximation of the trend in a moving time window. For further improving the robustness of the procedure, we investigate online outlier replacement by e.g. trimming or winsorization based on robust scale estimators. The performance of several versions of the procedure is compared in important data situations and applications to real and simulated data are given.

Keywords:

• Online monitoring
• Signal extraction
• Level shift
• Trend
• Outlier
• Bias curve

Acknowledgements

The author thanks Karen Schettlinger for complementary data analysis. The remarks of a referee, which were helpful to improve the presentation, and the financial support of the Deutsche Forschungsgemeinschaft (SFB 475, ‘Reduction of complexity in multivariate data structures’) are gratefully acknowledged.