Online signal extraction by robust regression in moving windows with data-adaptive width selection

Online (also 'real-time' or 'sequential') signal extraction from noisy and outlier-interfered data streams is a basic but challenging goal. Fitting a robust Repeated Median (Siegel in Biometrika 69:242-244, 1982) regression line in a moving time window has turned out to be a promising approach (Davies et al. in J. Stat. Plan. Inference 122:65-78, 2004; Gather et al. in Comput. Stat. 21:33-51, 2006; Schettlinger et al. in Biomed. Eng. 51:49-56, 2006). The level of the regression line at the rightmost window position, which equates to the current time point in an online application, is then used for signal extraction. However, the choice of the window width has a large impact on the signal extraction, and it is impossible to predetermine an optimal fixed window width for data streams which exhibit signal changes like level shifts and sudden trend changes. We therefore propose a robust test procedure for the online detection of such signal changes. An algorithm including the test allows for online window width adaption, meaning that the window width is chosen w.r.t. the current data situation at each time point. Comparison studies show that our new procedure outperforms an existing Repeated Median filter with automatic window width selection (Schettlinger et al. in Int. J. Adapt. Control Signal Process. 24:346-362, 2010).