{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T19:44:38Z","timestamp":1790711078904,"version":"4.1.0"},"reference-count":56,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2011,11,28]],"date-time":"2011-11-28T00:00:00Z","timestamp":1322438400000},"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":[[2012,8]]},"abstract":"<jats:p>Despite substantial criticism, variants of the capital asset pricing model (CAPM) remain to this day the primary statistical tools for portfolio managers to assess the performance of financial assets. In the CAPM, the risk of an asset is expressed through its correlation with the market, widely known as the beta. There is now a general consensus among economists that these portfolio betas are time-varying and that, consequently, any appropriate analysis has to take this variability into account. Recent advances in data acquisition and processing techniques have led to an increased research output concerning high-frequency models. Within this framework, we introduce here a modified functional CAPM and sequential monitoring procedures to test for the constancy of the portfolio betas. As our main results we derive the large-sample properties of these monitoring procedures. In a simulation study and an application to S&amp;P 100 data we show that our method performs well in finite samples.<\/jats:p>","DOI":"10.1017\/s0266466611000673","type":"journal-article","created":{"date-parts":[[2011,11,28]],"date-time":"2011-11-28T13:35:44Z","timestamp":1322487344000},"page":"804-837","source":"Crossref","is-referenced-by-count":43,"title":["SEQUENTIAL TESTING FOR THE STABILITY OF HIGH-FREQUENCY PORTFOLIO BETAS"],"prefix":"10.1017","volume":"28","author":[{"given":"Alexander","family":"Aue","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Siegfried","family":"H\u00f6rmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lajos","family":"Horv\u00e1th","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marie","family":"Hu\u0161kov\u00e1","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Josef G.","family":"Steinebach","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2011,11,28]]},"reference":[{"key":"S0266466611000673_ref3","doi-asserted-by":"publisher","DOI":"10.2307\/2938229"},{"key":"S0266466611000673_ref56","doi-asserted-by":"publisher","DOI":"10.1198\/016214505000000169"},{"key":"S0266466611000673_ref53","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0506715102"},{"key":"S0266466611000673_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1154-9"},{"key":"S0266466611000673_ref51","doi-asserted-by":"publisher","DOI":"10.1002\/0471264105"},{"key":"S0266466611000673_ref50","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466605050103"},{"key":"S0266466611000673_ref48","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1239\/jap\/1082999076","article-title":"Limit theorems for iterated random functions","volume":"41","author":"Shao","year":"2004","journal-title":"Journal of Applied Probability"},{"key":"S0266466611000673_ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2009.03.011"},{"key":"S0266466611000673_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(90)90099-F"},{"key":"S0266466611000673_ref19","article-title":"Delay time in monitoring jump changes in linear models","volume":"25","author":"\u010cernikov\u00e1","year":"2011","journal-title":"Statistics"},{"key":"S0266466611000673_ref2","first-page":"1","volume-title":"Advances in Econometrics: Econometric Analysis of Economic and Financial Time Series in Honor of R.F. Engle and C.W.J. Granger","volume":"B","author":"Andersen","year":"2006"},{"key":"S0266466611000673_ref44","first-page":"353","article-title":"Moment inequalities for the maximum of partial sums of random fields","volume":"39","author":"M\u00f3ricz","year":"1977","journal-title":"Acta Scientiarum Mathematicarum (Szeged)"},{"key":"S0266466611000673_ref52","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbankfin.2009.03.002"},{"key":"S0266466611000673_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s11749-006-0041-7"},{"key":"S0266466611000673_ref23","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600009063"},{"key":"S0266466611000673_ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2006.02.010"},{"key":"S0266466611000673_ref49","first-page":"424","article-title":"Capital asset prices: A theory of market equilibrium under conditions of risk","volume":"19","author":"Sharpe","year":"1964","journal-title":"Journal of Finance"},{"key":"S0266466611000673_ref11","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.3982\/ECTA6495","article-title":"Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise","volume":"76","author":"Barndorff-Nielsen","year":"2008","journal-title":"Econometrica"},{"key":"S0266466611000673_ref37","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466602186087"},{"key":"S0266466611000673_ref45","doi-asserted-by":"publisher","DOI":"10.2307\/1913610"},{"key":"S0266466611000673_ref7","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2006.00190.x"},{"key":"S0266466611000673_ref43","doi-asserted-by":"publisher","DOI":"10.2307\/1913811"},{"key":"S0266466611000673_ref54","doi-asserted-by":"publisher","DOI":"10.1214\/009117907000000060"},{"key":"S0266466611000673_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2010.07.009"},{"key":"S0266466611000673_ref31","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1991.tb03747.x"},{"key":"S0266466611000673_ref13","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2004.00515.x"},{"key":"S0266466611000673_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-405X(85)90004-2"},{"key":"S0266466611000673_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOS707"},{"key":"S0266466611000673_ref46","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466605050085"},{"key":"S0266466611000673_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2008.12.018"},{"key":"S0266466611000673_ref55","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v011.i10"},{"key":"S0266466611000673_ref4","doi-asserted-by":"publisher","DOI":"10.2307\/2951574"},{"key":"S0266466611000673_ref10","doi-asserted-by":"publisher","DOI":"10.1198\/073500108000000042"},{"key":"S0266466611000673_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/S0927-5398(97)00003-0"},{"key":"S0266466611000673_ref30","doi-asserted-by":"publisher","DOI":"10.1086\/296268"},{"key":"S0266466611000673_ref26","doi-asserted-by":"publisher","DOI":"10.1111\/0022-1082.224803"},{"key":"S0266466611000673_ref14","doi-asserted-by":"publisher","DOI":"10.1002\/jae.842"},{"key":"S0266466611000673_ref28","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466608090117"},{"key":"S0266466611000673_ref32","unstructured":"H\u00f6rmann S. , Horv\u00e1th L. , & Reeder R. (2010) Functional Volatility Sequences. Preprint, University of Utah."},{"key":"S0266466611000673_ref20","doi-asserted-by":"publisher","DOI":"10.2307\/2171955"},{"key":"S0266466611000673_ref42","doi-asserted-by":"publisher","DOI":"10.2469\/faj.v55.n4.2281"},{"key":"S0266466611000673_ref35","doi-asserted-by":"publisher","DOI":"10.1137\/1107036"},{"key":"S0266466611000673_ref36","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2008.11.004"},{"key":"S0266466611000673_ref38","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466698141038"},{"key":"S0266466611000673_ref40","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660999051X"},{"key":"S0266466611000673_ref21","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00091"},{"key":"S0266466611000673_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2004.01.002"},{"key":"S0266466611000673_ref39","doi-asserted-by":"publisher","DOI":"10.2307\/1924119"},{"key":"S0266466611000673_ref16","volume-title":"Convergence of Probability Measures","author":"Billingsley","year":"1968"},{"key":"S0266466611000673_ref17","doi-asserted-by":"publisher","DOI":"10.2307\/2109358"},{"key":"S0266466611000673_ref15","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466604206041"},{"key":"S0266466611000673_ref22","doi-asserted-by":"publisher","DOI":"10.1198\/073500102288618487"},{"key":"S0266466611000673_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/S0261-5606(98)00010-2"},{"key":"S0266466611000673_ref33","doi-asserted-by":"publisher","DOI":"10.1080\/10168730500381990"},{"key":"S0266466611000673_ref41","doi-asserted-by":"publisher","DOI":"10.1016\/0304-405X(87)90044-4"},{"key":"S0266466611000673_ref47","unstructured":"Santos A.O. (1998) Capital Asset Pricing Model and Changes in Volatility. Research paper 4, International Center for Financial Asset Management and Engineering."}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466611000673","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,25]],"date-time":"2019-04-25T19:10:59Z","timestamp":1556219459000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466611000673\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,11,28]]},"references-count":56,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["S0266466611000673"],"URL":"https:\/\/doi.org\/10.1017\/s0266466611000673","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,11,28]]}}}