{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T08:17:37Z","timestamp":1762503457484,"version":"build-2065373602"},"reference-count":34,"publisher":"Elsevier BV","issue":"10","license":[{"start":{"date-parts":[[2003,12,1]],"date-time":"2003-12-01T00:00:00Z","timestamp":1070236800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2003,12,1]],"date-time":"2003-12-01T00:00:00Z","timestamp":1070236800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"funder":[{"DOI":"10.13039\/501100001700","name":"Ministry of Education, Culture, Sports, Science and Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001700","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Neural Networks"],"published-print":{"date-parts":[[2003,12]]},"DOI":"10.1016\/s0893-6080(03)00188-6","type":"journal-article","created":{"date-parts":[[2003,7,31]],"date-time":"2003-07-31T21:57:13Z","timestamp":1059688633000},"page":"1527-1540","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":52,"title":["Polynomial harmonic GMDH learning networks for time series modeling"],"prefix":"10.1016","volume":"16","author":[{"given":"Nikolay Y.","family":"Nikolaev","sequence":"first","affiliation":[]},{"given":"Hitoshi","family":"Iba","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0893-6080(03)00188-6_BIB1","series-title":"Proceedings of the 20th symposium on the interface: computing science and statistics","first-page":"192","article-title":"Statistical learning networks: A unifying view","author":"Barron","year":"1988"},{"year":"1995","series-title":"Neural networks for pattern recognition","author":"Bishop","key":"10.1016\/S0893-6080(03)00188-6_BIB2"},{"year":"2000","series-title":"Fourier analysis of time series: An introduction","author":"Bloomfield","key":"10.1016\/S0893-6080(03)00188-6_BIB3"},{"year":"1997","series-title":"Numerical analysis","author":"Burden","key":"10.1016\/S0893-6080(03)00188-6_BIB4"},{"key":"10.1016\/S0893-6080(03)00188-6_BIB5","doi-asserted-by":"crossref","unstructured":"Chen, M. S., & Manry, M. T (1991). Power series analysis of backpropagation neural networks. In Proceedings of the international joint conference on neural networks, IJCNN'91 (Vol. I, pp. 295\u2013300).","DOI":"10.1109\/IJCNN.1991.155193"},{"issue":"4","key":"10.1016\/S0893-6080(03)00188-6_BIB6","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1109\/72.774207","article-title":"Function approximation\u2014a fast-convergence neural approach based on spectral analysis","volume":"10","author":"Citterio","year":"1999","journal-title":"IEEE Transactions on Neural Networks"},{"issue":"4","key":"10.1016\/S0893-6080(03)00188-6_BIB7","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1109\/72.80265","article-title":"The Stone\u2013Weierstrass theorem and its application to neural networks","volume":"1","author":"Cotter","year":"1990","journal-title":"IEEE Transactions on Neural Networks"},{"key":"10.1016\/S0893-6080(03)00188-6_BIB8","series-title":"Network models for control and processing","first-page":"143","article-title":"Induction and polynomial networks","author":"Elder","year":"2000"},{"year":"1999","series-title":"Nonparametric regression and spline smoothing","author":"Eubank","key":"10.1016\/S0893-6080(03)00188-6_BIB9"},{"key":"10.1016\/S0893-6080(03)00188-6_BIB10","series-title":"Artificial neural networks: Approximation and learning theory","first-page":"5","article-title":"There exists a neural network that does not make avoidable mistakes","author":"Gallant","year":"1992"},{"year":"1976","series-title":"Theory and application of the linear model","author":"Graybill","key":"10.1016\/S0893-6080(03)00188-6_BIB11"},{"key":"10.1016\/S0893-6080(03)00188-6_BIB12","doi-asserted-by":"crossref","first-page":"49","DOI":"10.2307\/2531895","article-title":"Statistical behavior of the GMDH algorithm","volume":"44","author":"Green","year":"1988","journal-title":"Biometrics"},{"year":"1991","series-title":"Introduction to the theory of neural computation","author":"Hertz","key":"10.1016\/S0893-6080(03)00188-6_BIB13"},{"year":"1987","series-title":"Introduction to numerical analysis","author":"Hildebrand","key":"10.1016\/S0893-6080(03)00188-6_BIB14"},{"key":"10.1016\/S0893-6080(03)00188-6_BIB17","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/0888-613X(93)90011-2","article-title":"A neuro-fuzzy approach to data analysis of pairwise comparisons","volume":"9","author":"Ichihashi","year":"1993","journal-title":"International Journal of Approximate Reasoning"},{"issue":"4","key":"10.1016\/S0893-6080(03)00188-6_BIB18","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1109\/TSMC.1971.4308320","article-title":"Polynomial theory of complex systems","volume":"1","author":"Ivakhnenko","year":"1971","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics"},{"year":"1983","series-title":"Time series","author":"Kendall","key":"10.1016\/S0893-6080(03)00188-6_BIB19"},{"year":"1999","series-title":"Elements of the theory of functions and functional analysis","author":"Kolmogorov","key":"10.1016\/S0893-6080(03)00188-6_BIB20"},{"key":"10.1016\/S0893-6080(03)00188-6_BIB21","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1016\/S0893-6080(98)00100-2","article-title":"On-line identification of nonlinear systems using Volterra polynomial basis function neural networks","volume":"11","author":"Liu","year":"1998","journal-title":"Neural Networks"},{"key":"10.1016\/S0893-6080(03)00188-6_BIB22","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1126\/science.267326","article-title":"Oscillation and chaos in physiological control systems","volume":"197","author":"Mackey","year":"1977","journal-title":"Science"},{"year":"1994","series-title":"Inductive learning algorithms for complex systems modeling","author":"Madala","key":"10.1016\/S0893-6080(03)00188-6_BIB23"},{"key":"10.1016\/S0893-6080(03)00188-6_BIB24","first-page":"261","article-title":"Three conjectures on neural network implementations of Volterra models","volume":"Vol. 3","author":"Marmarelis","year":"1994"},{"key":"10.1016\/S0893-6080(03)00188-6_BIB25","first-page":"243","article-title":"On the relation between Volterra models and feedforward artificial neural networks","volume":"Vol. 3","author":"Marmarelis","year":"1994"},{"key":"10.1016\/S0893-6080(03)00188-6_BIB26","unstructured":"Megson, J. M (1993). Systematic construction of trigonometric neural networks. Technical Report No. 416. University of Newcastle upon Tyne, UK."},{"key":"10.1016\/S0893-6080(03)00188-6_BIB27","first-page":"1048","article-title":"Networks with learned unit response functions","volume":"Vol. 4","author":"Moody","year":"1992"},{"year":"1994","series-title":"Classical and modern regression with applications","author":"Myers","key":"10.1016\/S0893-6080(03)00188-6_BIB28"},{"key":"10.1016\/S0893-6080(03)00188-6_BIB29","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/S0020-0255(97)10082-2","article-title":"Orthogonal and successive projection methods for the learning of neurofuzzy GMDH","volume":"110","author":"Ohtani","year":"1998","journal-title":"Information Sciences"},{"key":"10.1016\/S0893-6080(03)00188-6_BIB30","first-page":"318","article-title":"Learning internal representations by error propagation","volume":"Vol. 1","author":"Rumelhart","year":"1986"},{"key":"10.1016\/S0893-6080(03)00188-6_BIB31","doi-asserted-by":"crossref","unstructured":"Sakhnini, I. I., Manry, M. T., & Chandrasekaran, H (1999). Iterative improvement of trigonometric networks. In Proceedings of the international joint conference on neural networks, IJCNN'99, Washington, DC (pp. 1048\u20131055).","DOI":"10.1109\/IJCNN.1999.850721"},{"issue":"1","key":"10.1016\/S0893-6080(03)00188-6_BIB32","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1162\/neco.1991.3.1.67","article-title":"A tree-structured algorithm for reducing computation in networks with separable basis functions","volume":"3","author":"Sanger","year":"1991","journal-title":"Neural Computation"},{"year":"1980","series-title":"The Volterra and Wiener theories of nonlinear systems","author":"Schetzen","key":"10.1016\/S0893-6080(03)00188-6_BIB33"},{"issue":"1","key":"10.1016\/S0893-6080(03)00188-6_BIB34","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1109\/72.80209","article-title":"Self-organizing network for optimum supervised learning","volume":"1","author":"Tenorio","year":"1990","journal-title":"IEEE Transactions on Neural Networks"},{"key":"10.1016\/S0893-6080(03)00188-6_BIB35","series-title":"Nonlinear modeling and forecasting","first-page":"395","article-title":"Predicting sunspots and exchange rates with connectionist networks","author":"Weigend","year":"1992"},{"issue":"2","key":"10.1016\/S0893-6080(03)00188-6_BIB36","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1142\/S0129065700000119","article-title":"Higher order neural network group models for financial simulation","volume":"10","author":"Zhang","year":"2000","journal-title":"International Journal of Neural Systems"}],"container-title":["Neural Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893608003001886?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893608003001886?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:26:59Z","timestamp":1760232419000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0893608003001886"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,12]]},"references-count":34,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2003,12]]}},"alternative-id":["S0893608003001886"],"URL":"https:\/\/doi.org\/10.1016\/s0893-6080(03)00188-6","relation":{},"ISSN":["0893-6080"],"issn-type":[{"type":"print","value":"0893-6080"}],"subject":[],"published":{"date-parts":[[2003,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Polynomial harmonic GMDH learning networks for time series modeling","name":"articletitle","label":"Article Title"},{"value":"Neural Networks","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/S0893-6080(03)00188-6","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"converted-article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2003 Elsevier Ltd. All rights reserved.","name":"copyright","label":"Copyright"}]}}