RESEARCH ARTICLE


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.

Article Information


Identifiers and Pagination:

Year: 2009
Volume: 1
First Page: 43
Last Page: 51
Publisher Id: TOSPJ-1-43
DOI: 10.2174/1876527000901010043

Article History:

Received Date: 23/12/2008
Revision Received Date: 12/2/2009
Acceptance Date: 16/2/2009
Electronic publication date: 1/6/2009
Collection year: 2009

© 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: https://creativecommons.org/licenses/by/4.0/legalcode. 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: dtam@unt.edu


Abstract

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..