{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T13:33:28Z","timestamp":1768484008988,"version":"3.49.0"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,13]],"date-time":"2025-02-13T00:00:00Z","timestamp":1739404800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004442","name":"National Science Centre, Poland","doi-asserted-by":"publisher","award":["UMO-2022\/45\/B\/ST10\/01621"],"award-info":[{"award-number":["UMO-2022\/45\/B\/ST10\/01621"]}],"id":[{"id":"10.13039\/501100004442","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The concept of asymmetric persistence in time series was proposed and an appropriate stochastic Langevin-type model was presented. The influence of this particular form of memory on the behavior of the generated time series was examined. It has been shown that asymmetry causes a significant distortion of the effect of drift forces and has a weaker impact on stochastic diffusion forces. Due to this, the current known methods for reconstructing the Langevin-type model fail. The results of this work may help in deriving a new reconstruction method.<\/jats:p>","DOI":"10.3390\/sym17020287","type":"journal-article","created":{"date-parts":[[2025,2,13]],"date-time":"2025-02-13T08:01:19Z","timestamp":1739433679000},"page":"287","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Asymmetric Finite-Range Persistence in Time Series Generated by the Modified Discrete Langevin Model"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7806-6726","authenticated-orcid":false,"given":"Zbigniew","family":"Czechowski","sequence":"first","affiliation":[{"name":"Institute of Geophysics, Polish Academy of Sciences, 01-452 Warsaw, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,13]]},"reference":[{"key":"ref_1","unstructured":"Franses, P.H., and Paap, R. (2025, February 09). Modelling Asymmetric Persistence over the Business Cycle. Econometric Institute Research Papers (No. EI 9852). Available online: http:\/\/hdl.handle.net\/1765\/1525."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1080\/713665877","article-title":"Large returns, conditional correlation and portfolio diversification: A value-at-risk approach","volume":"1","author":"Silvapulle","year":"2001","journal-title":"Quant. Financ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1017\/S0022109000004294","article-title":"New evidence of asymmetric dependence structures in international equity Markets","volume":"43","author":"Okimoto","year":"2008","journal-title":"J. Financ. Quant. Anal."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/S0304-405X(02)00068-5","article-title":"Asymmetric correlations of equity portfolios","volume":"63","author":"Ang","year":"2002","journal-title":"J. Financ. Econ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1093\/rfs\/hhl037","article-title":"Asymmetries in stock returns: Statistical tests and economic evaluation","volume":"20","author":"Hong","year":"2007","journal-title":"Rev. Financ. Stud."},{"key":"ref_6","first-page":"437","article-title":"Modeling international financial returns with a multivariate regime switching copula","volume":"7","author":"Chollete","year":"2009","journal-title":"J. Financ. Econom."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1954","DOI":"10.1016\/j.jbankfin.2011.01.003","article-title":"Dependence structure and extreme comovements in international equity and bond markets","volume":"35","author":"Garcia","year":"2011","journal-title":"J. Bank. Financ."},{"key":"ref_8","unstructured":"Fitzgerald, W.J., Smith, R.L., Walden, A.T., and Young, P.C. (2000). A modelling framework for the prices and times of trades made on the New York stock exchange. Nonlinear and Nonstationary Signal Processing, Cambridge University Press."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.jeconom.2012.08.001","article-title":"Local Gaussian correlation: A new measure of dependence","volume":"172","author":"Hufthammer","year":"2013","journal-title":"J. Econom."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2263","DOI":"10.1016\/j.physa.2009.03.007","article-title":"A DFA approach for assessing asymmetric correlations","volume":"388","author":"Rodriguez","year":"2009","journal-title":"Phys. A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"043204","DOI":"10.1088\/1742-5468\/aab507","article-title":"The one-dimensional asymmetric persistent random walk","volume":"2018","author":"Rossetto","year":"2018","journal-title":"J. Stat. Mech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5592","DOI":"10.1016\/j.physa.2013.07.041","article-title":"Construction of A Langevin model from time series with a periodical correlation function: Application to wind speed data","volume":"392","author":"Czechowski","year":"2013","journal-title":"Phys. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"053109","DOI":"10.1063\/1.4951683","article-title":"Reconstruction of the modified discrete Langevin equation from persistent time series","volume":"26","author":"Czechowski","year":"2016","journal-title":"Chaos"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"063102","DOI":"10.1063\/5.0048598","article-title":"Discrete Langevin-type equation for p-order persistent time series and procedure of its reconstruction","volume":"31","author":"Czechowski","year":"2021","journal-title":"Chaos"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1088\/0034-4885\/29\/1\/306","article-title":"The Fluctuation-Dissipation Theorem","volume":"29","author":"Kubo","year":"1966","journal-title":"Rep. Prog. Phys."},{"key":"ref_16","first-page":"3","article-title":"Brownian motion and anomalous diffusion revisited via a fractional Langevin Equation","volume":"8","author":"Mainardi","year":"2009","journal-title":"Mod. Probl. State Phys."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Cao, L., Sun, R., Ma, T., and Liu, C. (2023). On Asymmetric Correlations and Their Applications in Financial Markets. J. Risk Financ. Manag., 16.","DOI":"10.3390\/jrfm16030187"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/S0378-4371(01)00144-3","article-title":"Detecting long-range correlations with detrended fluctuation analysis","volume":"295","author":"Kantelhardt","year":"2001","journal-title":"Phys. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0378-4371(02)01383-3","article-title":"Multifractal detrended fluctuation analysis of nonstationary time series","volume":"316","author":"Kantelhardt","year":"2002","journal-title":"Phys. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/S0375-9601(98)00283-7","article-title":"Analysis of data sets of stochastic systems","volume":"243","author":"Siegert","year":"1998","journal-title":"Phys. Lett. A"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Grasman, J., and van Herwaarden, O.A. (1999). Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications, Springer.","DOI":"10.1007\/978-3-662-03857-4"},{"key":"ref_22","unstructured":"Oksendal, B. (1998). Stochastic Differential Equations: An Introduction with Applications, Springer."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1137\/1010093","article-title":"Fractional Brownian Motions, Fractional Noises and Applications","volume":"10","author":"Mandelbrot","year":"1968","journal-title":"SIAM Rev."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/S0375-9601(02)01474-3","article-title":"A note on estimating drift and diffusion parameters from timeseries","volume":"305","author":"Sura","year":"2002","journal-title":"J. Phys. Lett. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"083034","DOI":"10.1088\/1367-2630\/10\/8\/083034","article-title":"On the definition and handling of different drift and diffusion estimates","volume":"10","author":"Gottschal","year":"2008","journal-title":"New J. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"031103","DOI":"10.1103\/PhysRevE.80.031103","article-title":"Arbitrary order corrections for finite-time drift and diffusion coefficients","volume":"80","author":"Anteneodo","year":"2009","journal-title":"Phys. Rev. E"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.physrep.2011.05.003","article-title":"Approaching complexity by stochastic methods: From biological systems to turbulence","volume":"506","author":"Friedrich","year":"2011","journal-title":"Phys. Rep."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/287\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:32:53Z","timestamp":1760027573000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/287"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,13]]},"references-count":27,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["sym17020287"],"URL":"https:\/\/doi.org\/10.3390\/sym17020287","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,13]]}}}