A method of fast update of absolute central sample moments of time series

The methods of updating central moments are often covered in various works where the large updating samples are present. However, absolute central moments of odd orders still remain unaddressed. In online systems and systems that are highly dependent on data transfer speed the issue of updating the absolute central moment of a time series on a certain constantly updating sample often comes up. In this paper we will propose a method for fast update of absolute central moments of time series and its programmatic implementation based on the treap data structure.