{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T11:42:24Z","timestamp":1649850144418},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2021,4,30]],"date-time":"2021-04-30T00:00:00Z","timestamp":1619740800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2022,4]]},"abstract":"<jats:p>This paper derives the limit distribution of the rescaled sum of the absolute value of an integrated process with continuously distributed innovations raised to a negative power less than <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S026646662100013X_inline1.png\" \/><jats:tex-math>\n$-$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>1, and of the analogous statistic that is obtained using the same function of an integrated process but only considering positive values of the integrated process. We show that the limit behavior of this statistic is determined by the values of the integrated process that are closest to 0, and find the limit behavior of the values of the integrated process that are closest to 0.<\/jats:p>","DOI":"10.1017\/s026646662100013x","type":"journal-article","created":{"date-parts":[[2021,4,30]],"date-time":"2021-04-30T07:57:48Z","timestamp":1619769468000},"page":"339-369","source":"Crossref","is-referenced-by-count":0,"title":["NEGATIVE POWERS OF INTEGRATED PROCESSES"],"prefix":"10.1017","volume":"38","author":[{"given":"Neslihan","family":"Sakarya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert M.","family":"de Jong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2021,4,30]]},"reference":[{"key":"S026646662100013X_r2","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466606060130"},{"key":"S026646662100013X_r8","volume-title":"An Introduction to Probability Theory and Its Applications","volume":"II","author":"Feller","year":"1971"},{"key":"S026646662100013X_r3","volume-title":"Proceedings of the Steklov Institute of Mathematics","volume":"195","author":"Borodin","year":"1995"},{"key":"S026646662100013X_r6","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466604203085"},{"key":"S026646662100013X_r7","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660505022X"},{"key":"S026646662100013X_r14","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466699153015"},{"key":"S026646662100013X_r10","doi-asserted-by":"publisher","DOI":"10.1214\/009117904000000658"},{"key":"S026646662100013X_r5","volume-title":"A Course in Probability Theory","author":"Chung","year":"2001"},{"key":"S026646662100013X_r4","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466608090476"},{"key":"S026646662100013X_r13","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"Miller","year":"1993"},{"key":"S026646662100013X_r9","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1931-1501604-6"},{"key":"S026646662100013X_r16","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466612000503"},{"key":"S026646662100013X_r11","doi-asserted-by":"publisher","DOI":"10.1186\/s40488-017-0059-2"},{"key":"S026646662100013X_r1","first-page":"57","article-title":"Comportement asymptotique du temps d\u2019occupation du processus des sommes partielles","volume":"29","author":"Akonom","year":"1993","journal-title":"Annales de l\u2019I.H.P. 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