{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:58:43Z","timestamp":1760147923034,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,11]],"date-time":"2023-03-11T00:00:00Z","timestamp":1678492800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Foundation of Korea funded by the Ministry of Education","award":["NRF-2017R1D1A1A09000804"],"award-info":[{"award-number":["NRF-2017R1D1A1A09000804"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper proposes a nonparametric directional dependence by using the local polynomial regression technique. With data generated from a bivariate copula having a nonmonotone regression structure, we show that our nonparametric directional dependence is superior to the copula directional dependence method in terms of the root-mean-square error. To validate the directional dependence with real data, we use the log returns of daily prices of Bitcoin, Ethereum, Ripple, and Stellar. We conclude that our nonparametric directional dependence, by using the local polynomial regression technique with asymmetric-threshold GARCH models for marginal distributions, detects the directional dependence better than the copula directional dependence method by an asymmetric GARCH model.<\/jats:p>","DOI":"10.3390\/axioms12030293","type":"journal-article","created":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T03:28:33Z","timestamp":1678678113000},"page":"293","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Nonparametric Directional Dependence Estimation and Its Application to Cryptocurrency"],"prefix":"10.3390","volume":"12","author":[{"given":"Hohsuk","family":"Noh","sequence":"first","affiliation":[{"name":"Department of Statistics, Sookmyung Women\u2019s University, Seoul 04310, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5173-8967","authenticated-orcid":false,"given":"Hyuna","family":"Jang","sequence":"additional","affiliation":[{"name":"Department of Statistics, Sookmyung Women\u2019s University, Seoul 04310, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kun Ho","family":"Kim","sequence":"additional","affiliation":[{"name":"John Molson School of Business, Concordia University, Montreal, QC H3H 0A1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3821-2060","authenticated-orcid":false,"given":"Jong-Min","family":"Kim","sequence":"additional","affiliation":[{"name":"Statistics Discipline, University of Minnesota-Morris, Morris, MN 56267, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kim, J.-M., Kim, S., and Kim, S.T. (2020). On the Relationship of Cryptocurrency Price with US Stock and Gold Price using Copula Models. Mathematics, 8.","DOI":"10.3390\/math8111859"},{"key":"ref_2","first-page":"229","article-title":"Fonctions de repartition an dimensions et leurs marges","volume":"8","author":"Sklar","year":"1959","journal-title":"Publ. Inst. Statist. Univ. Paris"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"R\u00fcschendorf, L., Schweizer, B., and Taylor, M.D. (1996). Distributions with Fixed Marginals and Related Topics, Institute of Mathematical Statistics.","DOI":"10.1214\/lnms\/1215452598"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1214\/aos\/1031689016","article-title":"Vines\u2014A new graphical model for dependent random variables","volume":"30","author":"Bedford","year":"2002","journal-title":"Ann. 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Anal."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1080\/01621459.2012.682850","article-title":"Pair Copula Constructions for Multivariate Discrete Data","volume":"107","author":"Panagiotelis","year":"2012","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1467","DOI":"10.1198\/jasa.2010.tm09572","article-title":"Modelling longitudinal data using a pair-copula decomposition of serial dependence","volume":"105","author":"Smith","year":"2010","journal-title":"J. Am. Stat."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1517","DOI":"10.1214\/12-EJS721","article-title":"Gaussian copula marginal regression","volume":"6","author":"Masarotto","year":"2012","journal-title":"Electron. J. 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