{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T00:21:51Z","timestamp":1789777311045,"version":"4.0.1"},"reference-count":22,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2016,11,19]],"date-time":"2016-11-19T00:00:00Z","timestamp":1479513600000},"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":[[2017,11,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We develop a complete methodology for detecting time varying or non-time-varying parameters in auto-regressive conditional heteroscedasticity (ARCH) processes. For this, we estimate and test various semiparametric versions of time varying ARCH models which include two well-known non-stationary ARCH-type models introduced in the econometrics literature. Using kernel estimation, we show that non-time-varying parameters can be estimated at the usual parametric rate of convergence and, for Gaussian noise, we construct estimates that are asymptotically efficient in a semiparametric sense. Then we introduce two statistical tests which can be used for detecting non-time-varying parameters or for testing the second-order dynamics. An information criterion for selecting the number of lags is also provided. We illustrate our methodology with several real data sets.<\/jats:p>","DOI":"10.1111\/rssb.12221","type":"journal-article","created":{"date-parts":[[2016,11,19]],"date-time":"2016-11-19T06:56:48Z","timestamp":1479538608000},"page":"1391-1414","source":"Crossref","is-referenced-by-count":21,"title":["Parameter Stability and Semiparametric Inference in Time Varying Auto-Regressive Conditional Heteroscedasticity Models"],"prefix":"10.1093","volume":"79","author":[{"given":"Lionel","family":"Truquet","sequence":"first","affiliation":[{"name":"University of Rennes and Ecole Nationale de la Statistique et de l'Analyse et de l'Information , Bruz , France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2016,11,19]]},"reference":[{"key":"2023022002192542500_rssb12221-cit-0001","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1111\/1468-0262.00114","article-title":"Inconsistency of the bootstrap when a parameter is on the boundary of the parameter space","volume":"68","author":"Andrews","year":"2000","journal-title":"Econometrica"},{"key":"2023022002192542500_rssb12221-cit-0002","volume-title":"Efficient and Adaptive Estimation for Semiparametric Models","author":"Bickel","year":"1998"},{"key":"2023022002192542500_rssb12221-cit-0003","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1111\/1467-9892.00296","article-title":"Estimating the ARCH parameters by solving linear equations","volume":"24","author":"Bose","year":"2003","journal-title":"J. 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