{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T10:01:11Z","timestamp":1790935271584,"version":"4.1.0"},"reference-count":62,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T00:00:00Z","timestamp":1783036800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T00:00:00Z","timestamp":1783036800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100008982","name":"National Science Foundation of Sri Lanka","doi-asserted-by":"publisher","award":["DMS\u20102310487"],"award-info":[{"award-number":["DMS\u20102310487"]}],"id":[{"id":"10.13039\/501100008982","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["J of Applied Econometrics"],"published-print":{"date-parts":[[2026,9]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>L\u00e9vy processes are widely used in financial modeling due to their ability to capture discontinuities and heavy tails, which are common in high\u2010frequency asset return data. However, parameter estimation remains a challenge when associated likelihoods are unavailable or costly to compute. We propose a fast and accurate method for L\u00e9vy parameter estimation using the neural Bayes estimation (NBE) framework\u2014a simulation\u2010based, likelihood\u2010free approach that leverages permutation\u2010invariant neural networks to approximate Bayes estimators. We contribute new theoretical results, showing that NBE results in consistent estimators whose risk converges to that of the Bayes estimator under mild conditions. Moreover, through extensive simulations across several L\u00e9vy models, we show that NBE outperforms traditional methods in both accuracy and runtime, while also enabling two complementary approaches to uncertainty quantification. We illustrate our approach on a challenging high\u2010frequency cryptocurrency return dataset, where the method captures evolving parameter dynamics and delivers reliable and interpretable inference at a fraction of the computational cost of traditional methods. We investigate nearly a decade of high\u2010frequency Bitcoin returns, requiring less than one minute to estimate parameters under the proposed approach.<\/jats:p>","DOI":"10.1002\/jae.70075","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T14:23:18Z","timestamp":1783088598000},"page":"862-876","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fast Likelihood\u2010Free Parameter Estimation for L\u00e9vy Processes"],"prefix":"10.1002","volume":"41","author":[{"given":"Nicolas","family":"Coloma","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics University of Colorado  Boulder Colorado USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"William","family":"Kleiber","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics University of Colorado  Boulder Colorado USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/jae.1105"},{"key":"e_1_2_10_3_1","first-page":"3731","volume-title":"IEEE International Conference on Big Data","author":"Banesh D.","year":"2021"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-8549-0_2"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1093\/genetics\/162.4.2025"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-12373-8"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/sta4.580"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600166010"},{"key":"e_1_2_10_9_1","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2015.1086656"},{"key":"e_1_2_10_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.qref.2019.09.011"},{"key":"e_1_2_10_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/10.554763"},{"key":"e_1_2_10_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ribaf.2019.101176"},{"key":"e_1_2_10_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11403-015-0168-2"},{"key":"e_1_2_10_14_1","volume-title":"Financial Modelling With Jump Processes","author":"Cont R.","year":"2004"},{"key":"e_1_2_10_15_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/91.3.729"},{"key":"e_1_2_10_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecosta.2016.11.008"},{"key":"e_1_2_10_17_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1984.tb01290.x"},{"key":"e_1_2_10_18_1","doi-asserted-by":"publisher","DOI":"10.1137\/15M1020575"},{"key":"e_1_2_10_19_1","unstructured":"Elgin H.2011.\u201cL\u00e9vy Processes and Parameter Estimation by Maximum Empirical Likelihood\u201d."},{"key":"e_1_2_10_20_1","doi-asserted-by":"publisher","DOI":"10.2307\/2287839"},{"key":"e_1_2_10_21_1","doi-asserted-by":"publisher","DOI":"10.1214\/09-LNMS5709"},{"key":"e_1_2_10_22_1","doi-asserted-by":"publisher","DOI":"10.1093\/molbev\/msy224"},{"key":"e_1_2_10_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.techfore.2020.119928"},{"key":"e_1_2_10_24_1","doi-asserted-by":"publisher","DOI":"10.3390\/e19100555"},{"key":"e_1_2_10_25_1","doi-asserted-by":"publisher","DOI":"10.1002\/sta4.382"},{"key":"e_1_2_10_26_1","doi-asserted-by":"publisher","DOI":"10.3390\/jrfm15010026"},{"key":"e_1_2_10_27_1","doi-asserted-by":"crossref","unstructured":"Han J. 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