{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T09:50:40Z","timestamp":1791366640334,"version":"4.3.1"},"reference-count":35,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2022,6,3]],"date-time":"2022-06-03T00:00:00Z","timestamp":1654214400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p>We consider high-frequency observations from a one-dimensional time-homogeneous diffusion process <jats:italic>Y<\/jats:italic>. We assume that the diffusion coefficient <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466622000214_inline1.png\"\/><jats:tex-math>\n$\\sigma $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is continuously differentiable in <jats:italic>y<\/jats:italic>, but with a jump discontinuity at some level <jats:italic>y<\/jats:italic>, say \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466622000214_inline2.png\"\/><jats:tex-math>\n$y=0$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. We first study sign-constrained kernel estimators of functions of the left and right limits of \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466622000214_inline3.png\"\/><jats:tex-math>\n$\\sigma $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> at \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466622000214_inline4.png\"\/><jats:tex-math>\n$0$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. These functions intricately depend on both limits. We propose a method to extricate these functions by searching for bandwidths where the kernel estimators are stable by iteration. We finally provide an estimator of the discontinuity jump size. We prove its convergence in probability and discuss its rate of convergence. A Monte Carlo study shows the finite sample properties of this estimator.<\/jats:p>","DOI":"10.1017\/s0266466622000214","type":"journal-article","created":{"date-parts":[[2022,6,3]],"date-time":"2022-06-03T06:13:26Z","timestamp":1654236806000},"page":"848-880","source":"Crossref","is-referenced-by-count":2,"title":["HOW LARGE IS THE JUMP DISCONTINUITY IN THE DIFFUSION COEFFICIENT OF A TIME-HOMOGENEOUS DIFFUSION?"],"prefix":"10.1017","volume":"39","author":[{"given":"Christian Y.","family":"Robert","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2022,6,3]]},"reference":[{"key":"S0266466622000214_r16","volume-title":"Brownian Motion and Stochastic Calculus","author":"Karatzas","year":"2000"},{"key":"S0266466622000214_r3","first-page":"183","article-title":"Occupation and local times for skew Brownian motion with applications to dispersion across an interface","volume":"21","author":"Appuhamillage","year":"2011a","journal-title":"The Annals of Applied Probability"},{"key":"S0266466622000214_r9","doi-asserted-by":"publisher","DOI":"10.1142\/S0219024906003937"},{"key":"S0266466622000214_r20","doi-asserted-by":"publisher","DOI":"10.1214\/154957807000000013"},{"key":"S0266466622000214_r17","doi-asserted-by":"publisher","DOI":"10.2307\/3213403"},{"key":"S0266466622000214_r24","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA12962"},{"key":"S0266466622000214_r1","volume-title":"High-Frequency Financial Econometrics","author":"Ait-Sahalia","year":"2014"},{"key":"S0266466622000214_r8","doi-asserted-by":"publisher","DOI":"10.1006\/tpbi.1998.1397"},{"key":"S0266466622000214_r2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809781"},{"key":"S0266466622000214_r22","doi-asserted-by":"publisher","DOI":"10.1051\/ps\/2018018"},{"key":"S0266466622000214_r19","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0099122"},{"key":"S0266466622000214_r33","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1997.tb02748.x"},{"key":"S0266466622000214_r5","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(03)00110-6"},{"key":"S0266466622000214_r11","doi-asserted-by":"publisher","DOI":"10.1111\/mafi.12120"},{"key":"S0266466622000214_r35","first-page":"52","volume-title":"Temps locaux","author":"Walsh","year":"1978"},{"key":"S0266466622000214_r23","doi-asserted-by":"publisher","DOI":"10.3150\/17-BEJ969"},{"key":"S0266466622000214_r21","doi-asserted-by":"publisher","DOI":"10.1111\/sjos.12033"},{"key":"S0266466622000214_r4","first-page":"2050","article-title":"Corrections: Occupation and local times for skew Brownian motion with applications to dispersion across an interface","volume":"21","author":"Appuhamillage","year":"2011b","journal-title":"The Annals of Applied Probability"},{"key":"S0266466622000214_r28","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-019-00406-2"},{"key":"S0266466622000214_r13","doi-asserted-by":"publisher","DOI":"10.1214\/09-AAP654"},{"key":"S0266466622000214_r30","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660808047X"},{"key":"S0266466622000214_r31","first-page":"293","article-title":"On stable sequences of events","volume":"25","author":"Renyi","year":"1963","journal-title":"Sankhya: The Indian Journal of Statistics, Series A (1961\u20132002)"},{"key":"S0266466622000214_r15","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6321.2004.00632.x"},{"key":"S0266466622000214_r7","doi-asserted-by":"publisher","DOI":"10.1214\/18-EJS1444"},{"key":"S0266466622000214_r32","first-page":"50","article-title":"Arbitrage in skew Brownian motion models","volume":"50","author":"Rossello","year":"2012","journal-title":"Insurance: Mathematics and Economics"},{"key":"S0266466622000214_r10","doi-asserted-by":"publisher","DOI":"10.2307\/3214513"},{"key":"S0266466622000214_r18","doi-asserted-by":"publisher","DOI":"10.1029\/1999WR900224"},{"key":"S0266466622000214_r29","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-10061-5"},{"key":"S0266466622000214_r6","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00395"},{"key":"S0266466622000214_r34","doi-asserted-by":"publisher","DOI":"10.1198\/jbes.2010.08342"},{"key":"S0266466622000214_r25","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2010.03.019"},{"key":"S0266466622000214_r27","first-page":"513","article-title":"On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations","volume":"9","author":"Nakao","year":"1972","journal-title":"Osaka Journal of Mathematics"},{"key":"S0266466622000214_r14","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600006101"},{"key":"S0266466622000214_r12","doi-asserted-by":"publisher","DOI":"10.1016\/S0246-0203(98)80026-5"},{"key":"S0266466622000214_r26","unstructured":"Mazzonetto, S. (2021) Rates of convergence to the local time of oscillating and skew Brownian motions. Preprint, arXiv:1912.04858."}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466622000214","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,4]],"date-time":"2023-08-04T09:40:11Z","timestamp":1691142011000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466622000214\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,3]]},"references-count":35,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["S0266466622000214"],"URL":"https:\/\/doi.org\/10.1017\/s0266466622000214","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,3]]}}}