{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T06:27:52Z","timestamp":1790144872378,"version":"4.0.1"},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2008,2,26]],"date-time":"2008-02-26T00:00:00Z","timestamp":1203984000000},"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":[[2008,6]]},"abstract":"<jats:p>We consider the parameter restrictions that need to be imposed to ensure that the conditional variance process of a GARCH(<jats:italic>p<\/jats:italic>,<jats:italic>q<\/jats:italic>) model remains nonnegative. Previously, Nelson and Cao (1992,<jats:italic>Journal of Business \u2019 Economic Statistics<\/jats:italic>10, 229\u2013235) provided a set of necessary and sufficient conditions for the aforementioned nonnegativity property for GARCH(<jats:italic>p<\/jats:italic>,<jats:italic>q<\/jats:italic>) models with<jats:italic>p<\/jats:italic>\u2264 2 and derived a sufficient condition for the general case of GARCH(<jats:italic>p<\/jats:italic>,<jats:italic>q<\/jats:italic>) models with<jats:italic>p<\/jats:italic>\u2265 3. In this paper, we show that the sufficient condition of Nelson and Cao (1992) for<jats:italic>p<\/jats:italic>\u2265 3 actually is also a necessary condition. In addition, we point out the linkage between the absolute monotonicity of the generalized autoregressive conditional heteroskedastic (GARCH) generating function and the nonnegativity of the GARCH kernel, and we use it to provide examples of sufficient conditions for this nonnegativity property to hold.<\/jats:p>","DOI":"10.1017\/s0266466608080432","type":"journal-article","created":{"date-parts":[[2008,2,26]],"date-time":"2008-02-26T11:15:46Z","timestamp":1204024546000},"page":"823-828","source":"Crossref","is-referenced-by-count":22,"title":["A NOTE ON INEQUALITY CONSTRAINTS IN THE GARCH MODEL"],"prefix":"10.1017","volume":"24","author":[{"given":"Henghsiu","family":"Tsai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kung-Sik","family":"Chan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2008,2,26]]},"reference":[{"key":"S0266466608080432_ref010","volume-title":"The Laplace Transform","author":"Widder","year":"1946"},{"key":"S0266466608080432_ref008","unstructured":"Tsai H. \u2019 Chan K.S. (2006) A Note on Inequality Constraints in the GARCH Model. Technical Report No. 361, Department of Statistics and Actuarial Science, University of Iowa; downloadable from http:\/\/1#x002F;techrep\/tr361.pdf."},{"key":"S0266466608080432_ref007","unstructured":"Titchmarsh E.C. (1939) The Theory of Functions, 2nd ed. Oxford University Press."},{"key":"S0266466608080432_ref006","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1080\/07350015.1992.10509902","article-title":"Inequality constraints in the univariate GARCH model","volume":"10","author":"Nelson","year":"1992","journal-title":"Journal of Business \u2019 Economic Statistics"},{"key":"S0266466608080432_ref004","volume-title":"An Introduction to Probability Theory and Its Applications","volume":"vol. 1","author":"Feller","year":"1968"},{"key":"S0266466608080432_ref003","doi-asserted-by":"publisher","DOI":"10.2307\/1912773"},{"key":"S0266466608080432_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90063-1"},{"key":"S0266466608080432_ref002","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbj015"},{"key":"S0266466608080432_ref005","unstructured":"Feller W. (1971) An Introduction to Probability Theory and Its Applications, vol. 2. Wiley."},{"key":"S0266466608080432_ref009","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.2006.00513.x"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466608080432","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T19:30:32Z","timestamp":1738092632000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466608080432\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,2,26]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,6]]}},"alternative-id":["S0266466608080432"],"URL":"https:\/\/doi.org\/10.1017\/s0266466608080432","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,2,26]]}}}