{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T14:58:44Z","timestamp":1766415524162},"reference-count":66,"publisher":"The Econometric Society","issue":"3","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>This paper studies inference for the realized Laplace transform (RLT) of volatility in a fixed\u2010span setting using bootstrap methods. Specifically, since standard wild bootstrap procedures deliver inconsistent inference, we propose a local Gaussian (LG) bootstrap, establish its first\u2010order asymptotic validity, and use Edgeworth expansions to show that the LG bootstrap inference achieves second\u2010order asymptotic refinements. Moreover, we provide new Laplace transform\u2010based estimators of the spot variance as well as the covariance, correlation, and beta between two semimartingales, and adapt our bootstrap procedure to the requisite scenario. We establish central limit theory for our estimators and first\u2010order asymptotic validity of their associated bootstrap methods. Simulations demonstrate that the LG bootstrap outperforms existing feasible inference theory and wild bootstrap procedures in finite samples. Finally, we illustrate the use of the new methods by examining the coherence between stocks and bonds during the global financial crisis of 2008 as well as the COVID\u201019 pandemic stock sell\u2010off during 2020, and by a forecasting exercise.<\/jats:p>","DOI":"10.3982\/qe1929","type":"journal-article","created":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T11:43:42Z","timestamp":1689594222000},"page":"1059-1103","source":"Crossref","is-referenced-by-count":3,"title":["Bootstrapping Laplace transforms of volatility"],"prefix":"10.3982","volume":"14","author":[{"given":"Ulrich","family":"Hounyo","sequence":"first","affiliation":[{"name":"Department of Economics, University at Albany\u2014State University of New York"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Macau"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rasmus T.","family":"Varneskov","sequence":"additional","affiliation":[{"name":"Department of Finance, Copenhagen Business School"},{"name":"Multi Assets, Nordea Asset Management"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2359","published-online":{"date-parts":[[2023]]},"reference":[{"key":"quan200286-bib-0001","doi-asserted-by":"crossref","first-page":"1744","DOI":"10.1080\/01621459.2016.1240082","volume":"112","author":"A\u00eft-Sahalia","year":"2017","journal-title":"Journal of the American Statistical Association"},{"key":"quan200286-bib-0002","volume-title":"High-Frequency Financial Econometrics","author":"A\u00eft-Sahalia","year":"2014"},{"key":"quan200286-bib-0003","first-page":"184","volume":"37","author":"A\u00eft-Sahalia","year":"2009","journal-title":"Annals of Statistics"},{"key":"quan200286-bib-0004","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s11203-011-9062-2","volume":"15","author":"Alvarez","year":"2012","journal-title":"Statistical Inference for Stochastic Processes"},{"key":"quan200286-bib-0005","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1198\/016214501750332965","volume":"96","author":"Andersen","year":"2001","journal-title":"Journal of the American Statistical Association"},{"key":"quan200286-bib-0006","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1111\/1468-0262.00418","volume":"71","author":"Andersen","year":"2003","journal-title":"Econometrica"},{"key":"quan200286-bib-0007","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1017\/S0266466618000373","volume":"35","author":"Andersen","year":"2019","journal-title":"Econometric Theory"},{"key":"quan200286-bib-0008","first-page":"1127","volume-title":"Handbook of the Economics of Finance","author":"Andersen","year":"2013"},{"key":"quan200286-bib-0009","volume-title":"Encyclopedia of Complexity and Systems Science","author":"Andersen","year":"2012"},{"issue":"3","key":"quan200286-bib-0010","doi-asserted-by":"crossref","first-page":"817","DOI":"10.2307\/2938229","volume":"59","author":"Andrews","year":"1991","journal-title":"Econometrica"},{"key":"quan200286-bib-0011","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.jfineco.2015.05.007","volume":"119","author":"Bandi","year":"2016","journal-title":"Journal of Financial Economics"},{"key":"quan200286-bib-0012","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1017\/S0266466617000457","volume":"34","author":"Bandi","year":"2018","journal-title":"Econometric Theory"},{"key":"quan200286-bib-0013","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.3982\/ECTA6495","volume":"76","author":"Barndorff-Nielsen","year":"2008","journal-title":"Econometrica"},{"key":"quan200286-bib-0014","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1111\/1467-9868.00336","volume":"64","author":"Barndorff-Nielsen","year":"2002","journal-title":"Journal of the Royal Statistical Society Series B"},{"key":"quan200286-bib-0015","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1111\/j.1468-0262.2004.00515.x","volume":"72","author":"Barndorff-Nielsen","year":"2004","journal-title":"Econometrica"},{"key":"quan200286-bib-0016","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/jjfinec\/nbh001","volume":"2","author":"Barndorff-Nielsen","year":"2004","journal-title":"Journal of Financial Econometrics"},{"key":"quan200286-bib-0017","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1080\/07350015.2017.1356728","volume":"37","author":"Bibinger","year":"2019","journal-title":"Journal of Business and Economic Statistics"},{"key":"quan200286-bib-0018","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jeconom.2015.10.007","volume":"192","author":"Bollerslev","year":"2016","journal-title":"Journal of Econometrics"},{"key":"quan200286-bib-0019","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.jfineco.2018.02.011","volume":"128","author":"Campbell","year":"2018","journal-title":"Journal of Financial Economics"},{"key":"quan200286-bib-0020","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1016\/j.jeconom.2006.07.013","volume":"140","author":"Carrasco","year":"2007","journal-title":"Journal of Econometrics"},{"key":"quan200286-bib-0021","unstructured":"Casini, Alessandro and Pierre Perron (2019), \u201cContinuous record Laplace-based inference about the break date in structural change models.\u201d Unpublished manuscript, Boston University."},{"key":"quan200286-bib-0022","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1111\/1467-9965.00057","volume":"8","author":"Comte","year":"1998","journal-title":"Mathematical Finance"},{"key":"quan200286-bib-0023","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1093\/jjfinec\/nbp001","volume":"7","author":"Corsi","year":"2009","journal-title":"Journal of Financial Econometrics"},{"key":"quan200286-bib-0024","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1080\/01621459.2018.1447485","volume":"114","author":"Dovonon","year":"2019","journal-title":"Journal of the American Statistical Association"},{"key":"quan200286-bib-0025","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1257\/0002828041464597","volume":"94","author":"Engle","year":"2004","journal-title":"The American Economic Review"},{"issue":"1","key":"quan200286-bib-0026","doi-asserted-by":"crossref","first-page":"139","DOI":"10.2307\/2171927","volume":"64","author":"Foster","year":"1996","journal-title":"Econometrica"},{"key":"quan200286-bib-0027","first-page":"283","volume":"1","author":"Gon\u00e7alves","year":"2009","journal-title":"Econometrica"},{"key":"quan200286-bib-0028","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4384-7","volume-title":"The Bootstrap and Edgeworth Expansion","author":"Hall","year":"1992"},{"key":"quan200286-bib-0029","doi-asserted-by":"crossref","first-page":"453","DOI":"10.3982\/ECTA5771","volume":"79","author":"Hansen","year":"2011","journal-title":"Econometrica"},{"key":"quan200286-bib-0030","doi-asserted-by":"crossref","first-page":"359","DOI":"10.3150\/bj\/1116340299","volume":"11","author":"Hayashi","year":"2005","journal-title":"Bernoulli"},{"key":"quan200286-bib-0031","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.jeconom.2016.11.002","volume":"197","author":"Hounyo","year":"2017","journal-title":"Journal of Econometrics"},{"key":"quan200286-bib-0032","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1017\/S0266466618000129","volume":"35","author":"Hounyo","year":"2019","journal-title":"Econometric Theory"},{"key":"quan200286-bib-0033","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1017\/S0266466616000281","volume":"33","author":"Hounyo","year":"2017","journal-title":"Econometric Theory"},{"key":"quan200286-bib-0034","doi-asserted-by":"crossref","unstructured":"Hounyo, Ulrich, Zhi Liu, and Rasmus T. Varneskov (2022), \u201cA modified wild bootstrap procedure for Laplace transforms of volatility.\u201d Unpublished manuscript. https:\/\/papers.ssrn.com\/sol3\/papers.cfm?abstract_id=4187049.","DOI":"10.2139\/ssrn.4187049"},{"key":"quan200286-bib-0035","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.jeconom.2017.01.002","volume":"198","author":"Hounyo","year":"2017","journal-title":"Journal of Econometrics"},{"key":"quan200286-bib-0036","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jeconom.2019.09.001","volume":"215","author":"Hounyo","year":"2020","journal-title":"Journal of Econometrics"},{"key":"quan200286-bib-0037","doi-asserted-by":"crossref","unstructured":"Hounyo, Ulrich, Zhi Liu, and Rasmus T. Varneskov (2023), \u201cSupplement to \u2018Bootstrapping Laplace transforms of volatility\u2019.\u201d Quantitative Economics Supplemental Material, 14, https:\/\/doi.org\/10.3982\/QE1929.","DOI":"10.2139\/ssrn.4414552"},{"key":"quan200286-bib-0038","first-page":"1462","volume":"41","author":"Jacod","year":"2013","journal-title":"Annals of Statistics"},{"key":"quan200286-bib-0039","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1007\/978-3-319-11605-1_20","volume-title":"Large Deviations and Asymptotic Methods in Finance","author":"Jacod","year":"2015"},{"key":"quan200286-bib-0040","first-page":"1029","volume":"42","author":"Jacod","year":"2014","journal-title":"Annals of Statistics"},{"issue":"7","key":"quan200286-bib-0041","doi-asserted-by":"crossref","first-page":"2249","DOI":"10.1016\/j.spa.2008.11.004","volume":"119","author":"Jacod","year":"2009","journal-title":"Stochastic Processes and their Applications"},{"key":"quan200286-bib-0042","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-24127-7","volume-title":"Discretization of Processes","author":"Jacod","year":"2012"},{"key":"quan200286-bib-0043","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1198\/073500102317351958","volume":"20","author":"Jiang","year":"2002","journal-title":"Journal of Business and Economic Statistics"},{"key":"quan200286-bib-0044","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1017\/S0266466609090616","volume":"26","author":"Kristensen","year":"2010","journal-title":"Econometric Theory"},{"key":"quan200286-bib-0045","doi-asserted-by":"crossref","first-page":"2535","DOI":"10.1093\/rfs\/hhm056","volume":"21","author":"Lee","year":"2008","journal-title":"Review of Financial Studies"},{"key":"quan200286-bib-0046","first-page":"156","volume":"47","author":"Li","year":"2019","journal-title":"Annals of Statistics"},{"key":"quan200286-bib-0047","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.jeconom.2017.01.010","volume":"200","author":"Li","year":"2017","journal-title":"Journal of Econometrics"},{"key":"quan200286-bib-0048","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.jeconom.2016.01.004","volume":"193","author":"Li","year":"2016","journal-title":"Journal of Econometrics"},{"key":"quan200286-bib-0049","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.3982\/ECTA12306","volume":"84","author":"Li","year":"2016","journal-title":"Econometrica"},{"issue":"6","key":"quan200286-bib-0050","doi-asserted-by":"crossref","first-page":"1958","DOI":"10.1016\/j.spa.2017.08.015","volume":"128","author":"Liu","year":"2018","journal-title":"Stochastic Processes and their Applications"},{"key":"quan200286-bib-0051","doi-asserted-by":"crossref","unstructured":"Liu, Qiang and Zhi Liu (2020), \u201cStatistical inference of spot correlation and spot market beta under infinite variation jumps.\u201d Journal of Financial Econometrics. (forthcoming).","DOI":"10.1093\/jjfinec\/nbaa028"},{"key":"quan200286-bib-0052","first-page":"1696","volume":"16","author":"Liu","year":"1988","journal-title":"Annals of Statistics"},{"key":"quan200286-bib-0053","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1111\/j.1467-9469.2008.00622.x","volume":"36","author":"Mancini","year":"2009","journal-title":"Scandinavian Journal of Statistics"},{"key":"quan200286-bib-0054","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s11203-009-9037-8","volume":"13","author":"Podolskij","year":"2010","journal-title":"Statistical Inference for Stochastic Processes"},{"key":"quan200286-bib-0055","doi-asserted-by":"crossref","first-page":"2955","DOI":"10.1016\/j.spa.2015.02.008","volume":"125","author":"Reiss","year":"2015","journal-title":"Stochastic Processes and their Applications"},{"key":"quan200286-bib-0056","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0795-5","volume-title":"The Jackknife and the Bootstrap","author":"Shao","year":"1995"},{"key":"quan200286-bib-0057","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1111\/1468-0262.00071","volume":"67","author":"Sims","year":"1999","journal-title":"Econometrica"},{"key":"quan200286-bib-0058","doi-asserted-by":"crossref","first-page":"1831","DOI":"10.1214\/15-AOS1327","volume":"43","author":"Todorov","year":"2015","journal-title":"Annals of Statistics"},{"key":"quan200286-bib-0059","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/j.jeconom.2011.06.016","volume":"164","author":"Todorov","year":"2011","journal-title":"Journal of Econometrics"},{"key":"quan200286-bib-0060","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1080\/01621459.2012.682854","volume":"107","author":"Todorov","year":"2012","journal-title":"Journal of the American Statistical Association"},{"key":"quan200286-bib-0061","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.3982\/ECTA9133","volume":"80","author":"Todorov","year":"2012","journal-title":"Econometrica"},{"key":"quan200286-bib-0062","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1017\/S0266466616000475","volume":"33","author":"Varneskov","year":"2017","journal-title":"Econometric Theory"},{"key":"quan200286-bib-0063","doi-asserted-by":"crossref","first-page":"920","DOI":"10.1111\/sjos.12365","volume":"46","author":"Wang","year":"2019","journal-title":"Scandinavian Journal of Statistics"},{"key":"quan200286-bib-0064","first-page":"1261","volume":"14","author":"Wu","year":"1986","journal-title":"Annals of Statistics"},{"key":"quan200286-bib-0065","doi-asserted-by":"crossref","first-page":"1394","DOI":"10.1198\/016214505000000169","volume":"100","author":"Zhang","year":"2005","journal-title":"Journal of the American Statistical Association"},{"key":"quan200286-bib-0066","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.jeconom.2014.04.001","volume":"181","author":"Zu","year":"2014","journal-title":"Journal of Econometrics"}],"container-title":["Quantitative Economics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.3982\/QE1929","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T11:47:18Z","timestamp":1689594438000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.econometricsociety.org\/doi\/10.3982\/QE1929"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"references-count":66,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023]]}},"alternative-id":["10.3982\/QE1929"],"URL":"https:\/\/doi.org\/10.3982\/qe1929","relation":{},"ISSN":["1759-7323"],"issn-type":[{"value":"1759-7323","type":"print"}],"subject":[],"published":{"date-parts":[[2023]]}}}