{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:23:18Z","timestamp":1760242998261,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2015,4,28]],"date-time":"2015-04-28T00:00:00Z","timestamp":1430179200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we propose a nonparametric statistical tool to identify the most relevant lag in the model description of a time series. It is also shown that it can be used for model identification. The statistic is based on the number of runs, when the time series is symbolized depending on the empirical quantiles of the time series. With a Monte Carlo simulation, we show the size and power performance of our new test statistic under linear and nonlinear data generating processes. From the theoretical point of view, it is the first time that symbolic analysis and runs are proposed to identifying characteristic lags and also to help in the identification of univariate time series models. From a more applied point of view, the results show the power and competitiveness of the proposed tool with respect to other techniques without presuming or specifying a model.<\/jats:p>","DOI":"10.3390\/e17052706","type":"journal-article","created":{"date-parts":[[2015,4,29]],"date-time":"2015-04-29T04:42:57Z","timestamp":1430282577000},"page":"2706-2722","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Identifying the Most Relevant Lag with Runs"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6373-9433","authenticated-orcid":false,"given":"\u00darsula","family":"Faura","sequence":"first","affiliation":[{"name":"Departamento de M\u00e9todos Cuantitativos para la Econom\u00eda y la Empresa, Universidad de Murcia, Espinardo 30100, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matilde","family":"Lafuente","sequence":"additional","affiliation":[{"name":"Departamento de M\u00e9todos Cuantitativos para la Econom\u00eda y la Empresa, Universidad de Murcia, Espinardo 30100, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mariano","family":"Matilla-Garc\u00eda","sequence":"additional","affiliation":[{"name":"Departamento de Econom\u00eda A. Cuantitativa I, Universidad Nacional de Educaci\u00f3n a Distancia (UNED), Madrid 28040, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manuel","family":"Ruiz","sequence":"additional","affiliation":[{"name":"Department of Quantitative Methods, Universidad Polit\u00e9cnica de Cartagena, Cartagena 30203, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,4,28]]},"reference":[{"key":"ref_1","unstructured":"Granger, C., and Weiss, A. (1983). Studies in Econometrics, Time Series, and Multivariate Statistics, Academic Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1080\/02331889708802564","article-title":"Measures and tests of independence: A survey","volume":"28","author":"Tjostheim","year":"1996","journal-title":"Statistics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1111\/j.1467-9892.1994.tb00200.x","article-title":"Using the mutual information coefficient to identify lags in nonlinear models","volume":"15","author":"Granger","year":"1994","journal-title":"J. Time Series Anal."},{"key":"ref_4","first-page":"1410","article-title":"Nonparametric identification of nonlinear time series: Selecting significant lags","volume":"89","author":"Tjostheim","year":"1994","journal-title":"J. Am. Statist. Assoc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.econlet.2009.04.014","article-title":"Detection of non-linear structure in time series","volume":"105","year":"2009","journal-title":"Econ. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"046212","DOI":"10.1103\/PhysRevE.82.046212","article-title":"Permutation-information-theory approach to unveil delay dynamics from time-series analysis","volume":"82","author":"Zunino","year":"2010","journal-title":"Phys. Rev. E"},{"key":"ref_7","first-page":"242","article-title":"Time Scales of a Chaotic Semiconductor Laser with Optical Feedback Under the Lens of a Permutation Information Analysis","volume":"42","author":"Soriano","year":"2011","journal-title":"IEEE J. Quant. Electr."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1713","DOI":"10.1364\/OE.22.001713","article-title":"Mapping the dynamic complexity of a semiconductor laser with optical feedback using permutation entropy","volume":"22","author":"Toomey","year":"2014","journal-title":"Opt. Express"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Amigo, J.M. (2010). Permutation Complexity in Dynamical Systems, Springer.","DOI":"10.1007\/978-3-642-04084-9"},{"key":"ref_10","unstructured":"Shannon, C.E., and Weaver, W. (1949). The Mathematical Theory of Communication, University of Illinois Press."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1090\/S0002-9947-1921-1501161-8","article-title":"Recursive geodesic on a surface of negative curvature","volume":"22","author":"Morse","year":"1949","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_12","unstructured":"Collet, P., and Eckmann, J.P. (1980). Iterated Maps on the Interval as Dynamical Systems, Brickhauser."},{"key":"ref_13","first-page":"123","article-title":"Nonparametric Tests for Serial Dependence Based on Runs","volume":"18","author":"Faura","year":"2014","journal-title":"Dyn. Psychol. Life Sci."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2706\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:45:30Z","timestamp":1760215530000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2706"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,28]]},"references-count":13,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2015,5]]}},"alternative-id":["e17052706"],"URL":"https:\/\/doi.org\/10.3390\/e17052706","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2015,4,28]]}}}