{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T09:57:10Z","timestamp":1700215030991},"reference-count":26,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2006,2]]},"abstract":" We improve the least squares (LS) method for building models of a nonlinear dynamical system given finite time series which are contaminated by observational noise. When the noise level is low, the LS method gives good estimates for the parameters, however, the models selected as the best by information criteria often tend to be over-parameterized or even degenerate. We observe that the correct model is not selected as the best model despite belonging to the chosen model class. To overcome this, we propose a simple but very effective idea to use the LS method more appropriately. We apply the method for model selection. Numerical studies indicate that the method can be used to apply information criteria more effectively, and generally avoid over-fitting and model degeneracy. <\/jats:p>","DOI":"10.1142\/s0218127406014927","type":"journal-article","created":{"date-parts":[[2006,4,10]],"date-time":"2006-04-10T11:53:16Z","timestamp":1144669996000},"page":"445-464","source":"Crossref","is-referenced-by-count":5,"title":["MODELING NONLINEAR TIME SERIES USING IMPROVED LEAST SQUARES METHOD"],"prefix":"10.1142","volume":"16","author":[{"given":"TOMOMICHI","family":"NAKAMURA","sequence":"first","affiliation":[{"name":"Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China"}]},{"given":"MICHAEL","family":"SMALL","sequence":"additional","affiliation":[{"name":"Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(01)00313-X"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1974.1100705"},{"key":"rf3","volume-title":"Advanced Econometrics","author":"Amemiya T.","year":"1985"},{"key":"rf4","first-page":"133","volume":"156","author":"Atten P.","journal-title":"J. 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