A multi-scale approach for testing and detecting peaks in time series

Abstract

An approach is presented that combines a statistical test for peak detection with the estimation of peak positions in time series. Motivated by empirical observations in neuronal recordings, we aim at investigating peaks of different heights and widths. We use a moving window approach to compare the differences of estimated slope coefficients of local regression models. We combine multiple windows and use the global maximum of all different processes as a test statistic. After rejection, a multiple filter algorithm combines peak positions estimated from multiple windows. Analysing neuronal activity recorded in anaesthetized mice, the procedure could identify significant differences between two brain states concerning peak occurrences and intermediate down states showing no peaks. This suggests that the method can be useful in the analysis of time series showing variability of peak shapes. The method is implemented in the (Formula presented.) -package (Formula presented.) (available on CRAN).