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.
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David C. Tam (2009) studied this question.
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