Multi-dimensional sparse time series: feature extraction

TL;DR

This paper introduces a novel method for analyzing multi-dimensional sparse time series using entropy and linguistic techniques, enabling classification, clustering, and prediction of complex data like economic measurements.

Contribution

It defines new markers based on entropy and linguistic analysis for encoding and understanding multi-dimensional time series behavior.

Findings

Markers effectively characterize series dynamics and trends.

Application to economic data demonstrates practical utility.

Markers facilitate classification and prediction tasks.

Abstract

We show an analysis of multi-dimensional time series via entropy and statistical linguistic techniques. We define three markers encoding the behavior of the series, after it has been translated into a multi-dimensional symbolic sequence. The leading component and the trend of the series with respect to a mobile window analysis result from the entropy analysis and label the dynamical evolution of the series. The diversification formalizes the differentiation in the use of recurrent patterns, from a Zipf law point of view. These markers are the starting point of further analysis such as classification or clustering of large database of multi-dimensional time series, prediction of future behavior and attribution of new data. We also present an application to economic data. We deal with measurements of money investments of some business companies in advertising market for different media sources.