A Theoretical Analysis of Cumulative Sum Slope (CUSUM-Slope) Statistic for Detecting Signal Onset (begin) and Offset (end) Trends from Background Noise Level

David Tam*
Department of Biological Sciences, University of North Texas, Denton, Texas 76203, USA.

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© 2009 Tam et al.;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Biological Sciences, University of North Texas, Denton, Texas 76203, USA. E-mail:


A theoretical analysis of the cumulative sum (CUSUM) technique for detecting a series of time signals from noisy background is provided. The statistic using CUSUM-slope is introduced as a measure for capturing the average of signals within the time-window, in which the slope is computed. This provides a time-independent method for estimating the signal content within the time-window. The detection criterion is provided for different window-lengths. The results showed that this CUSUM-slope statistic is highly sensitive to the detection of subtle hidden trends in the data sequence with noise filtered even in very low signal-to-noise environment.

Keywords: Cumulative sum, CUSUM, Signal detection, Noise filtering, Serial dependence, Trend analysis, Time-series analysis..