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This paper fills the gap by proposing a novel conditional heteroskedastic model called \u201cquantile double autoregression\u201d. The strict stationarity of the new model is derived, and self-weighted conditional quantile estimation is suggested. Two promising properties of the original double autoregressive model are shown to be preserved. Based on the quantile autocorrelation function and self-weighting concept, three portmanteau tests are constructed to check the adequacy of the fitted conditional quantiles. The finite sample performance of the proposed inferential tools is examined by simulation studies, and the need for use of the new model is further demonstrated by analyzing the S&amp;P500 Index.<\/jats:p>","DOI":"10.1017\/s026646662100030x","type":"journal-article","created":{"date-parts":[[2021,6,25]],"date-time":"2021-06-25T09:13:47Z","timestamp":1624612427000},"page":"793-839","source":"Crossref","is-referenced-by-count":10,"title":["QUANTILE DOUBLE AUTOREGRESSION"],"prefix":"10.1017","volume":"38","author":[{"given":"Qianqian","family":"Zhu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guodong","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2021,6,25]]},"reference":[{"key":"S026646662100030X_r4","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-842X.1975.tb01366.x"},{"key":"S026646662100030X_r6","volume-title":"Time 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