{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T08:17:40Z","timestamp":1790756260331,"version":"4.1.0"},"reference-count":31,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2003,7,8]],"date-time":"2003-07-08T00:00:00Z","timestamp":1057622400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003,8,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Standard goodness-of-fit tests for a parametric regression model against a series of nonparametric alternatives are based on residuals arising from a fitted model. When a parametric regression model is compared with a nonparametric model, goodness-of-fit testing can be naturally approached by evaluating the likelihood of the parametric model within a nonparametric framework. We employ the empirical likelihood for an \u03b1-mixing process to formulate a test statistic that measures the goodness of fit of a parametric regression model. The technique is based on a comparison with kernel smoothing estimators. The empirical likelihood formulation of the test has two attractive features. One is its automatic consideration of the variation that is associated with the nonparametric fit due to empirical likelihood's ability to Studentize internally. The other is that the asymptotic distribution of the test statistic is free of unknown parameters, avoiding plug-in estimation. We apply the test to a discretized diffusion model which has recently been considered in financial market analysis.<\/jats:p>","DOI":"10.1111\/1467-9868.00408","type":"journal-article","created":{"date-parts":[[2003,7,8]],"date-time":"2003-07-08T13:37:41Z","timestamp":1057671461000},"page":"663-678","source":"Crossref","is-referenced-by-count":85,"title":["An Empirical Likelihood Goodness-of-Fit Test for Time Series"],"prefix":"10.1093","volume":"65","author":[{"given":"Song Xi","family":"Chen","sequence":"first","affiliation":[{"name":"National University of Singapore , Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wolfgang","family":"H\u00e4rdle","sequence":"additional","affiliation":[{"name":"Humboldt-Universit\u00e4t zu Berlin , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ming","family":"Li","sequence":"additional","affiliation":[{"name":"National University of Singapore , Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2003,7,8]]},"reference":[{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1093\/rfs\/9.2.385","article-title":"Testing continuous-time models of the spot interest rate","volume":"9","author":"A\u00eft-Sahalia","year":"1996","journal-title":"Rev. Finan. Stud."},{"key":"2023040706272593500_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1718-3","article-title":"Nonparametric statistics for stochastic processes","volume":"110","author":"Bosq","year":"1998","journal-title":"Lect. Notes Statist."},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1093\/biomet\/83.2.329","article-title":"Empirical likelihood for nonparametric density estimation","volume":"83","author":"Chen","year":"1996","journal-title":"Biometrika"},{"key":"2023040706272593500_","volume-title":"Research Report 3\/2001","author":"Chen","year":"2002"},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"385","DOI":"10.2307\/1911242","article-title":"A theory of term structure of interest rates","volume":"53","author":"Cox","year":"1985","journal-title":"Econometrica"},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1080\/01621459.1990.10476211","article-title":"Testing the goodness of fit of a linear model via nonparametric regression techniques","volume":"85","author":"Eubank","year":"1990","journal-title":"J. Am. Statist. Ass."},{"key":"2023040706272593500_","volume-title":"Research Report","author":"Fan","year":"2000"},{"key":"2023040706272593500_","article-title":"Estimation and model specification testing in nonparametric and semiparametric time series econometric models","author":"Gao","year":"2001","journal-title":"Technical Report"},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.2307\/3318471","article-title":"Stochastic Volatility models as hidden markov models and statistical applications","volume":"6","author":"Genon-Catalot","year":"2000","journal-title":"Bernoulli"},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1137\/1122049","article-title":"On the strong mixing property for linear sequences","volume":"22","author":"Gorodeskii","year":"1977","journal-title":"Theory Probab. Applic."},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"109","DOI":"10.2307\/1403462","article-title":"Methodology and algorithms of empirical likelihood","volume":"58","author":"Hall","year":"1990","journal-title":"Int. Statist. Rev."},{"key":"2023040706272593500_","volume-title":"Discussion Paper","author":"H\u00e4rdle","year":"2000"},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"1926","DOI":"10.1214\/aos\/1176349403","article-title":"Comparing nonparametric versus parametric regression fits","volume":"21","author":"H\u00e4rdle","year":"1993","journal-title":"Ann. Statist."},{"key":"2023040706272593500_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2722-7","volume-title":"Nonparametric Smoothing and Lack-of-fit Tests","author":"Hart","year":"1997"},{"key":"2023040706272593500_","volume-title":"Discussion Paper","author":"Hjellvik","year":"1996"},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/S0378-3758(97)00146-8","article-title":"Linearity testing using local polynomial approximation","volume":"68","author":"Hjellvik","year":"1998","journal-title":"J. Statist. Planng. Inf."},{"key":"2023040706272593500_","volume-title":"Research Report","author":"Hong","year":"2001"},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1111\/1468-0262.00207","article-title":"An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative","volume":"69","author":"Horowitz","year":"2001","journal-title":"Econometrica"},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"2084","DOI":"10.1214\/aos\/1069362388","article-title":"Empirical likelihood methods with weakly dependent processes","volume":"25","author":"Kitamura","year":"1997","journal-title":"Ann. Statist."},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1214\/aos\/1018031108","article-title":"Nonparametric model checks for time series","volume":"27","author":"Koul","year":"1999","journal-title":"Ann. Statist."},{"key":"2023040706272593500_","volume-title":"Discussion Paper","author":"Kreiss","year":"1998"},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1017\/S0266466600009166","article-title":"Nonparametric estimation and identification of nonlinear arch time series","volume":"11","author":"Masry","year":"1995","journal-title":"Econometr. Theory"},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1093\/biomet\/84.2.395","article-title":"Empirical likelihood confidence regions in time series models","volume":"84","author":"Monti","year":"1997","journal-title":"Biometrika"},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1214\/aos\/1176347494","article-title":"Empirical likelihood ratio confidence regions","volume":"18","author":"Owen","year":"1990","journal-title":"Ann. Statist."},{"key":"2023040706272593500_","volume-title":"Empirical Likelihood","author":"Owen","year":"2001"},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/0304-4149(85)90031-6","article-title":"Some mixing properties of time series models","volume":"19","author":"Pham","year":"1985","journal-title":"Stoch. Process. Applic."},{"key":"2023040706272593500_","volume-title":"Preprint","author":"Platen","year":"1999"},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1214\/aos\/1176325370","article-title":"Empirical likelihood and general estimating functions","volume":"22","author":"Qin","year":"1994","journal-title":"Ann. Statist."},{"key":"2023040706272593500_","volume-title":"Research Report","author":"Tripathi","year":"2000"},{"key":"2023040706272593500_","first-page":"409","article-title":"Simulation of stationary Gaussian process in [0,1]d","volume":"3","author":"Wood","year":"1994","journal-title":"J. Comput. Graph. Statist."},{"key":"2023040706272593500_","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/BF00532676","article-title":"Limiting behaviour of U-Statistics for stationary absolutely regular processes","volume":"35","author":"Yoshihara","year":"1976","journal-title":"Z. Wahrsch. Ver. Geb."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2F1467-9868.00408","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2F1467-9868.00408","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/65\/3\/663\/49795346\/jrsssb_65_3_663.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/65\/3\/663\/49795346\/jrsssb_65_3_663.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,10]],"date-time":"2024-01-10T07:39:25Z","timestamp":1704872365000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/65\/3\/663\/7110682"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,7,8]]},"references-count":31,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2003,7,8]]},"published-print":{"date-parts":[[2003,8,1]]}},"URL":"https:\/\/doi.org\/10.1111\/1467-9868.00408","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2003,8]]},"published":{"date-parts":[[2003,7,8]]}}}