Composite Multiscale Partial Cross-Sample Entropy Analysis for Quantifying Intrinsic Similarity of Two Time Series Affected by Common External Factors.

Baogen Li,Guosheng Han,Shan Jiang,Zuguo Yu,Zuguo Yu

doi:10.3390/e22091003

Abstract

In this paper, we propose a new cross-sample entropy, namely the composite multiscale partial cross-sample entropy (CMPCSE), for quantifying the intrinsic similarity of two time series affected by common external factors. First, in order to test the validity of CMPCSE, we apply it to three sets of artificial data. Experimental results show that CMPCSE can accurately measure the intrinsic cross-sample entropy of two simultaneously recorded time series by removing the effects from the third time series. Then CMPCSE is employed to investigate the partial cross-sample entropy of Shanghai securities composite index (SSEC) and Shenzhen Stock Exchange Component Index (SZSE) by eliminating the effect of Hang Seng Index (HSI). Compared with the composite multiscale cross-sample entropy, the results obtained by CMPCSE show that SSEC and SZSE have stronger similarity. We believe that CMPCSE is an effective tool to study intrinsic similarity of two time series.

Highlights

Complex systems with interacting constituents exist in all aspects of nature and society, such as geophysics [1], solid state physics, climate system, ecosystem, financial system [2,3], and so forth.These complex systems are constantly generating a large number of time signals
Inspired by the above works, we propose the composite multiscale partial cross-sample entropy (CMPCSE) to measure the intrinsic similarity of two time series affected by the third common external factor simultaneously in this paper
Based on composite multiscale cross-sample entropy (CMCSE) [26], we propose a new method-composite multiscale partial cross-sample entropy (CMPCSE), which can be used to quantify the intrinsic similarity of two time series linearly affected by a common external factor

Summary

Introduction

Complex systems with interacting constituents exist in all aspects of nature and society, such as geophysics [1], solid state physics, climate system, ecosystem, financial system [2,3], and so forth. Cross-sample entropy (Cross-SampEn) was proposed for comparing two different time series to assess their degree of similarity [15]. In 2018, in order to better study the time series from the stock market, Wu and his coworkers introduced modified multiscale sample entropy measure based on symbolic representation and similarity (MSEBSS) [28]. Wang et al proposed multiscale cross-trend sample entropy (MCTSE) to study the similarity of two time series that with potential trends [29]. Inspired by the above works, we propose the composite multiscale partial cross-sample entropy (CMPCSE) to measure the intrinsic similarity of two time series affected by the third common external factor simultaneously in this paper. We first test CMPCSE on three sets of artificial data, and find that it can reveal the intrinsic similarity of the time series come from the models, and apply it to a set of stock market indices

Composite Multiscale Partial Cross-Sample Entropy

Numerical Experiments for Artificial Time Series

TWO-Component ARFIMA Process

Multifractal Binomial Measures

Application to Stock Market Index

Discussion and Conclusions