{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T02:57:47Z","timestamp":1791514667413,"version":"4.3.4"},"reference-count":35,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2016,6,28]],"date-time":"2016-06-28T00:00:00Z","timestamp":1467072000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"Chaire Autorit\u00e9 de Contr\u00f4le Prudentiel et de R\u00e9solution \u2018Regulation and systemic risk\u2019"},{"name":"Global Risk Institute"},{"name":"French Agence Nationale de la Recherche via project PRAM","award":["ANR-10-ORAR-008-01"],"award-info":[{"award-number":["ANR-10-ORAR-008-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,6,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>The non-causal auto-regressive process with heavy-tailed errors has non-linear causal dynamics, which allow for local explosion or asymmetric cycles that are often observed in economic and financial time series. It provides a new model for multiple local explosions in a strictly stationary framework. The causal predictive distribution displays surprising features, such as higher moments than for the marginal distribution, or the presence of a unit root in the Cauchy case. Aggregating such models can yield complex dynamics with local and global explosion as well as variation in the rate of explosion. The asymptotic behaviour of a vector of sample auto-correlations is studied in a semiparametric non-causal AR(1) framework with Pareto-like tails, and diagnostic tests are proposed. Empirical results based on the Nasdaq composite price index are provided.<\/jats:p>","DOI":"10.1111\/rssb.12193","type":"journal-article","created":{"date-parts":[[2016,6,29]],"date-time":"2016-06-29T05:06:46Z","timestamp":1467176806000},"page":"737-756","source":"Crossref","is-referenced-by-count":78,"title":["Local Explosion Modelling by Non-Causal Process"],"prefix":"10.1093","volume":"79","author":[{"given":"Christian","family":"Gouri\u00e9roux","sequence":"first","affiliation":[{"name":"Centre de Recherche en Economie et Statistique , Malakoff , France"},{"name":"University of Toronto , Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Michel","family":"Zako\u00efan","sequence":"additional","affiliation":[{"name":"Centre de Recherche en Economie et Statistique , Malakoff"},{"name":"Universit \u00b4e de Lille , France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2016,6,28]]},"reference":[{"key":"2023021709323128200_rssb12193-cit-0001","doi-asserted-by":"crossref","first-page":"1946","DOI":"10.1214\/08-AOS632","article-title":"Maximum likelihood estimation for \u03b1-stable autoregressive process","volume":"37","author":"Andrews","year":"2009","journal-title":"Ann. 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