{"title":"Study on Coded Permutation Entropy of Finite Length Gaussian White Noise Time Series","authors":"Huihui Sun;Xiaofeng Zhang;Lin Wang","doi":"10.23919/cje.2022.00.209","DOIUrl":null,"url":null,"abstract":"As an extension of permutation entropy (PE), coded permutation entropy (CPE) improves the performance of PE by making a secondary division for ordinal patterns defined in PE. In this study, we provide an exploration of the statistical properties of CPE using a finite length Gaussian white noise time series theoretically. By means of the Taylor series expansion, the approximate expressions of the expected value and variance of CPE are deduced and the Cramér-Rae low bound (CRLB) is obtained to evaluate the performance of the CPE estimator. The results indicate that CPE is a biased estimator, but the bias only depends on relevant parameters of CPE and it can be easily corrected for an arbitrary time series. The variance of CPE is related to the encoding patterns distribution, and the value converges to the CRLB of the CPE estimator when the time series length is large enough. For a finite-length Gaussian white noise time series model, the predicted values can match well with the actual values, which further validates the statistic theory of CPE. Using the theoretical expressions of CPE, it is possible to better understand the behavior of CPE for most of the time series.","PeriodicalId":50701,"journal":{"name":"Chinese Journal of Electronics","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10410594","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chinese Journal of Electronics","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10410594/","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
As an extension of permutation entropy (PE), coded permutation entropy (CPE) improves the performance of PE by making a secondary division for ordinal patterns defined in PE. In this study, we provide an exploration of the statistical properties of CPE using a finite length Gaussian white noise time series theoretically. By means of the Taylor series expansion, the approximate expressions of the expected value and variance of CPE are deduced and the Cramér-Rae low bound (CRLB) is obtained to evaluate the performance of the CPE estimator. The results indicate that CPE is a biased estimator, but the bias only depends on relevant parameters of CPE and it can be easily corrected for an arbitrary time series. The variance of CPE is related to the encoding patterns distribution, and the value converges to the CRLB of the CPE estimator when the time series length is large enough. For a finite-length Gaussian white noise time series model, the predicted values can match well with the actual values, which further validates the statistic theory of CPE. Using the theoretical expressions of CPE, it is possible to better understand the behavior of CPE for most of the time series.
期刊介绍:
CJE focuses on the emerging fields of electronics, publishing innovative and transformative research papers. Most of the papers published in CJE are from universities and research institutes, presenting their innovative research results. Both theoretical and practical contributions are encouraged, and original research papers reporting novel solutions to the hot topics in electronics are strongly recommended.