期刊名称：International Journal of Applied Mathematics and Computer Science
电子版ISSN：2083-8492
出版年度：2019
卷号：29
期号：1
页码：1-12
DOI：10.2478/amcs-2019-0015
出版社：De Gruyter Open
摘要：High-order cumulant tensors carry information about statistics of non-normally distributed multivariate data. In this work
we present a new efficient algorithm for calculation of cumulants of arbitrary orders in a sliding window for data streams.
We show that this algorithm offers substantial speedups of cumulant updates compared with the current solutions. The
proposed algorithm can be used for processing on-line high-frequency multivariate data and can find applications, e.g.,
in on-line signal filtering and classification of data streams. To present an application of this algorithm, we propose an
estimator of non-Gaussianity of a data stream based on the norms of high order cumulant tensors. We show how to detect
the transition from Gaussian distributed data to non-Gaussian ones in a data stream. In order to achieve high implementation
efficiency of operations on super-symmetric tensors, such as cumulant tensors, we employ a block structure to store and
calculate only one hyper-pyramid part of such tensors.
关键词：high order cumulants; time;series statistics; non;normally distributed data; data streaming;
