Working Paper Article Version 3 This version is not peer-reviewed

# Distribution-Based Entropy Weighting Clustering of Skewed and Heavy-Tailed Time Series

Version 1 : Received: 30 March 2021 / Approved: 2 April 2021 / Online: 2 April 2021 (18:41:16 CEST)
Version 2 : Received: 6 April 2021 / Approved: 7 April 2021 / Online: 7 April 2021 (17:45:03 CEST)
Version 3 : Received: 24 May 2021 / Approved: 28 May 2021 / Online: 28 May 2021 (13:51:14 CEST)

A peer-reviewed article of this Preprint also exists.

Mattera, R.; Giacalone, M.; Gibert, K. Distribution-Based Entropy Weighting Clustering of Skewed and Heavy Tailed Time Series. Symmetry 2021, 13, 959. Mattera, R.; Giacalone, M.; Gibert, K. Distribution-Based Entropy Weighting Clustering of Skewed and Heavy Tailed Time Series. Symmetry 2021, 13, 959.

## Abstract

The goal of clustering is to identify common structures in a data set by forming groups of homogeneous objects. The observed characteristics of many economic time series motivated the development of classes of distributions that can accommodate properties such as heavy tails and skewness. Thanks to its flexibility, the Skewed Exponential Power Distribution (also called Skewed Generalized Error Distribution) ensures a unified and general framework for clustering possibly skewed and heavy tailed time series. This paper develops a clustering procedure of model-based type, assuming that the time series are generated by the same underlying probability distribution but with different parameters. Moreover, we propose to optimally combine the estimated parameters to form the clusters with an entropy weighing $k$-means approach. The usefulness of the proposal is showed by means of application to financial time series, demonstrating also how the obtained clusters can be used to form portfolio of stocks.

## Keywords

Classification; Generalized Error Distribution; Skewness; Skewed Exponential Power Distribution; Portfolio selection

## Subject

Computer Science and Mathematics, Probability and Statistics

Comment 1
Commenter: Massimiliano Giacalone
Commenter's Conflict of Interests: Author
Comment: Updated version after revisions.
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