{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T22:14:28Z","timestamp":1790201668034,"version":"4.1.0"},"reference-count":71,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2010,2,17]],"date-time":"2010-02-17T00:00:00Z","timestamp":1266364800000},"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":[[2010,10]]},"abstract":"<jats:p>In this paper we analyze the asymptotic properties of the popular distribution tail index estimator by Hill (1975) for dependent, heterogeneous processes. We develop new extremal dependence measures that characterize a massive array of linear, nonlinear, and conditional volatility processes with long or short memory. We prove that the Hill estimator is weakly and uniformly weakly consistent for processes with extremes that form mixingale sequences and asymptotically normal for processes with extremes that are near epoch dependent (NED) on some arbitrary mixing functional. The extremal persistence assumptions in this paper are known to hold for mixing,<jats:italic>L<jats:sub>p<\/jats:sub><\/jats:italic>-NED, and some non-<jats:italic>L<jats:sub>p<\/jats:sub><\/jats:italic>-NED processes, including ARFIMA, FIGARCH, explosive GARCH, nonlinear ARMA-GARCH, and bilinear processes, and nonlinear distributed lags like random coefficient and regime-switching autoregressions.<\/jats:p><jats:p>Finally, we deliver a simple nonparametric estimator of the asymptotic variance of the Hill estimator and prove consistency for processes with NED extremes.<\/jats:p>","DOI":"10.1017\/s0266466609990624","type":"journal-article","created":{"date-parts":[[2010,2,17]],"date-time":"2010-02-17T11:40:45Z","timestamp":1266406845000},"page":"1398-1436","source":"Crossref","is-referenced-by-count":81,"title":["ON TAIL INDEX ESTIMATION FOR DEPENDENT, HETEROGENEOUS DATA"],"prefix":"10.1017","volume":"26","author":[{"given":"Jonathan B.","family":"Hill","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2010,2,17]]},"reference":[{"key":"S0266466609990624_ref71","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1016\/j.spa.2005.01.001","article-title":"On linear processes with dependent innovations","volume":"115","author":"Wu","year":"2005","journal-title":"Stochastic Processes and Their Applications"},{"key":"S0266466609990624_ref70","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0506715102"},{"key":"S0266466609990624_ref66","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177698240"},{"key":"S0266466609990624_ref65","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9469.00301"},{"key":"S0266466609990624_ref63","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2008.03.003"},{"key":"S0266466609990624_ref62","doi-asserted-by":"crossref","first-page":"1156","DOI":"10.1214\/aoap\/1028903376","article-title":"Tail index estimation for dependent data","volume":"8","author":"Resnick","year":"1998","journal-title":"Annals of Applied Probability"},{"key":"S0266466609990624_ref61","doi-asserted-by":"publisher","DOI":"10.2307\/3214926"},{"key":"S0266466609990624_ref60","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1214\/aoap\/1019487509","article-title":"Self-Similar communication models and very heavy tails","volume":"10","author":"Resnick","year":"2000","journal-title":"Annals of Applied Probability"},{"key":"S0266466609990624_ref58","doi-asserted-by":"publisher","DOI":"10.1111\/1467-937X.00184"},{"key":"S0266466609990624_ref57","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1214\/aos\/1176343003","article-title":"Statistical-Inference using extreme order statistics","volume":"3","author":"Pickands","year":"1975","journal-title":"Annals of Statistics"},{"key":"S0266466609990624_ref56","doi-asserted-by":"publisher","DOI":"10.2307\/1913610"},{"key":"S0266466609990624_ref55","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.2007.00562.x"},{"key":"S0266466609990624_ref54","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996269"},{"key":"S0266466609990624_ref53","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996608"},{"key":"S0266466609990624_ref52","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176993783"},{"key":"S0266466609990624_ref51","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.2005.00412.x"},{"key":"S0266466609990624_ref50","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5449-2"},{"key":"S0266466609990624_ref45","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176349409"},{"key":"S0266466609990624_ref36","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346596"},{"key":"S0266466609990624_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012780"},{"key":"S0266466609990624_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466602181023"},{"key":"S0266466609990624_ref40","unstructured":"Hill J.B. 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