Measures median as more and more outliers are included in the calculation according to a specified rule, of outliers being furthest from the mean.

outlierinclude_mdrmd(y, zscored = TRUE)



the input time series (ideally z-scored)


Should y be z-scored before computing the statistic. Default: TRUE


median of the median of range indices


The threshold for including time-series data points in the analysis increases from zero to the maximum deviation, in increments of 0.01*sigma (by default), where sigma is the standard deviation of the time series.

At each threshold, proportion of time series points included and median are calculated, and outputs from the algorithm measure how these statistical quantities change as more extreme points are included in the calculation.

Outliers are defined as furthest from the mean.


B.D. Fulcher and N.S. Jones. hctsa: A computational framework for automated time-series phenotyping using massive feature extraction. Cell Systems 5, 527 (2017).

B.D. Fulcher, M.A. Little, N.S. Jones Highly comparative time-series analysis: the empirical structure of time series and their methods. J. Roy. Soc. Interface 10, 83 (2013).


Yangzhuoran Yang