{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T18:43:58Z","timestamp":1726425838515},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T00:00:00Z","timestamp":1287360000000},"content-version":"unspecified","delay-in-days":8235,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1988,4]]},"abstract":"<jats:p>In this paper, it will be shown that if we condition a <jats:italic>k<\/jats:italic>-variate rational-valued time series process on its entire past, it is possible to capture all relevant information on the past of the process by a single random variable. This scalar random variable can be formed as an autoregressive moving average of past observations; Since economic data are usually reported in a finite number of digits, this result applies to virtually all economic time series. Therefore, economic time series regressions generally take the form of a nonlinear function of an autoregressive moving average of past observations. This approach is applied to model specification testing of nonlinear ARX models.<\/jats:p>","DOI":"10.1017\/s0266466600011816","type":"journal-article","created":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T05:12:04Z","timestamp":1287378724000},"page":"35-59","source":"Crossref","is-referenced-by-count":7,"title":["ARMA Memory Index Modeling of Economic Time Series"],"prefix":"10.1017","volume":"4","author":[{"given":"Herman J.","family":"Bierens","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2010,10,18]]},"reference":[{"key":"S0266466600011816_ref010","doi-asserted-by":"publisher","DOI":"10.2307\/3315046"},{"volume-title":"Linear operators, Part I., General theory","year":"1957","author":"Dunford","key":"S0266466600011816_ref013"},{"key":"S0266466600011816_ref003","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9574.1982.tb00777.x"},{"key":"S0266466600011816_ref001","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600011014"},{"key":"S0266466600011816_ref020","doi-asserted-by":"publisher","DOI":"10.2307\/1912017"},{"volume-title":"Real analysis","year":"1968","author":"Royden","key":"S0266466600011816_ref018"},{"key":"S0266466600011816_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(82)90102-6"},{"key":"S0266466600011816_ref011","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344949"},{"key":"S0266466600011816_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(84)90025-3"},{"key":"S0266466600011816_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-45529-2"},{"key":"S0266466600011816_ref017","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346150"},{"key":"S0266466600011816_ref016","first-page":"451","volume-title":"Analysis and optimization of stochastic systems","author":"Rissanen","year":"1980"},{"key":"S0266466600011816_ref015","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(78)90005-5"},{"key":"S0266466600011816_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(87)90086-8"},{"key":"S0266466600011816_ref019","first-page":"45","volume-title":"New Methods in Business Cycle Research; Proceedings from a Conference","author":"Sargent","year":"1977"},{"key":"S0266466600011816_ref022","doi-asserted-by":"publisher","DOI":"10.2307\/1911465"},{"volume-title":"A course in probability theory","year":"1974","author":"Chung","key":"S0266466600011816_ref009"},{"key":"S0266466600011816_ref021","first-page":"283","volume-title":"Large-scale macro-econometric models","author":"Sims","year":"1981"},{"key":"S0266466600011816_ref004","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1983.10478031"},{"volume-title":"Independent and stationary sequences of random variables","year":"1971","author":"Ibragimov","key":"S0266466600011816_ref014"},{"volume-title":"Convergence of probability measures","year":"1968","author":"Billingsley","key":"S0266466600011816_ref008"},{"key":"S0266466600011816_ref006","doi-asserted-by":"publisher","DOI":"10.1017\/CCOL0521344301.003"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600011816","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T16:04:53Z","timestamp":1558368293000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600011816\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,4]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1988,4]]}},"alternative-id":["S0266466600011816"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600011816","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"type":"print","value":"0266-4666"},{"type":"electronic","value":"1469-4360"}],"subject":[],"published":{"date-parts":[[1988,4]]}}}