{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T11:47:06Z","timestamp":1759664826872},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2008,7,4]],"date-time":"2008-07-04T00:00:00Z","timestamp":1215129600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2009,6]]},"DOI":"10.1007\/s11222-008-9078-7","type":"journal-article","created":{"date-parts":[[2008,7,3]],"date-time":"2008-07-03T16:22:29Z","timestamp":1215102149000},"page":"149-153","source":"Crossref","is-referenced-by-count":7,"title":["A note on the non-negativity of continuous-time ARMA and GARCH processes"],"prefix":"10.1007","volume":"19","author":[{"given":"Henghsiu","family":"Tsai","sequence":"first","affiliation":[]},{"given":"Kung-Sik","family":"Chan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,7,4]]},"reference":[{"key":"9078_CR1","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S0304-4076(96)01819-2","volume":"77","author":"T.G. Andersen","year":"1997","unstructured":"Andersen, T.G., Lund, J.: Estimating continuous-time stochastic volatility models of the short-term interest rate. J. Econom. 77, 343\u2013377 (1997)","journal-title":"J. Econom."},{"key":"9078_CR2","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1111\/1467-9868.00282","volume":"63","author":"O.E. Barndorff-Nielsen","year":"2001","unstructured":"Barndorff-Nielsen, O.E., Shephard, N.: Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics (with discussion). J. R. Stat. Soc. Ser. B 63, 167\u2013241 (2001)","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"9078_CR3","volume-title":"A Treatise on Differential Equations","author":"G. Boole","year":"1872","unstructured":"Boole, G.: A Treatise on Differential Equations. Macmillan and Co., London (1872)"},{"key":"9078_CR4","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1142\/9781848160156_0001","volume-title":"Statistics and Finance: An Interface","author":"P.J. Brockwell","year":"2000","unstructured":"Brockwell, P.J.: Heavy-tailed and non-linear continuous-time ARMA models for financial time series. In: Chan, W.S., Li, W.K., Tong, H. (eds.) Statistics and Finance: An Interface, pp. 3\u201322. Imperial College Press, London (2000)"},{"key":"9078_CR5","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1023\/A:1017972605872","volume":"53","author":"P.J. Brockwell","year":"2001","unstructured":"Brockwell, P.J.: L\u00e9vy-driven CARMA processes. Ann. Inst. Stat. Math. 53, 113\u2013124 (2001)","journal-title":"Ann. Inst. Stat. Math."},{"key":"9078_CR6","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1239\/jap\/1082552212","volume":"41A","author":"P.J. Brockwell","year":"2004","unstructured":"Brockwell, P.J.: Representations of continuous-time ARMA processes. J. Appl. Probab. 41A, 375\u2013382 (2004)","journal-title":"J. Appl. Probab."},{"key":"9078_CR7","doi-asserted-by":"crossref","first-page":"790","DOI":"10.1214\/105051606000000150","volume":"16","author":"P.J. Brockwell","year":"2006","unstructured":"Brockwell, P.J., Chadraa, E., Lindner, A.: Continuous time GARCH processes. Ann. Appl. Probab. 16, 790\u2013826 (2006)","journal-title":"Ann. Appl. Probab."},{"key":"9078_CR8","first-page":"477","volume":"15","author":"P.J. Brockwell","year":"2005","unstructured":"Brockwell, P.J., Marquardt, T.: L\u00e9vy-driven and fractionally integrated ARMA processes with continuous time parameter. Stat. Sin. 15, 477\u2013494 (2005)","journal-title":"Stat. Sin."},{"key":"9078_CR9","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1111\/1467-9965.00057","volume":"8","author":"F. Comte","year":"1998","unstructured":"Comte, F., Renault, E.: Long memory in continuous-time stochastic volatility models. Math. Finance 8, 291\u2013323 (1998)","journal-title":"Math. Finance"},{"key":"9078_CR10","unstructured":"Finkel, D.E., Kelley, C.T.: Convergence analysis of the DIRECT algorithm. Technical Report CRSC-TR04-28, Center for Research in Scientific Computation, North Carolina State University (2004). Available at www.optimization-online.org\/DB_FILE\/2004\/08\/934.pdf"},{"key":"9078_CR11","unstructured":"Gablonsky, J.M.: DIRECT version 2.0. User Guide. Technical Report CRSC-TR01-08, Center for Research in Scientific Computation, North Carolina University (2001)"},{"key":"9078_CR12","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1023\/A:1017930332101","volume":"21","author":"J.M. Gablonsky","year":"2001","unstructured":"Gablonsky, J.M., Kelley, C.T.: A locally-biased form of the DIRECT algorithm. J. Glob. Optim. 21, 27\u201337 (2001)","journal-title":"J. Glob. Optim."},{"key":"9078_CR13","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/BF00941892","volume":"79","author":"D.R. Jones","year":"1993","unstructured":"Jones, D.R., Perttunen, C.D., Stuckmann, B.E.: Lipschitzian optimization without the Lipschitz constant. J. Optim. Theory Appl. 79, 157\u2013181 (1993)","journal-title":"J. Optim. Theory Appl."},{"key":"9078_CR14","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970920","volume-title":"Iterative Methods for Optimization","author":"C.T. Kelley","year":"1999","unstructured":"Kelley, C.T.: Iterative Methods for Optimization. SIAM, Philadelphia (1999)"},{"key":"9078_CR15","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1239\/jap\/1091543413","volume":"41","author":"C. Kl\u00fcppelberg","year":"2004","unstructured":"Kl\u00fcppelberg, C., Lindner, A., Maller, R.: A continuous time GARCH process driven by a L\u00e9vy process: stationarity and second order behaviour. J. Appl. Probab. 41, 601\u2013622 (2004)","journal-title":"J. Appl. Probab."},{"key":"9078_CR16","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1111\/j.1369-7412.2004.05139.x","volume":"66","author":"G.O. Roberts","year":"2004","unstructured":"Roberts, G.O., Papaspiliopoulos, O., Dellaportas, P.: Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes. J. R. Stat. Soc. Ser. B 66, 369\u2013393 (2004)","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"9078_CR17","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1198\/073500106000000260","volume":"24","author":"V. Todorov","year":"2006","unstructured":"Todorov, V., Tauchen, G.: Simulation methods for L\u00e9vy-driven CARMA stochastic volatility models. J. Bus. Econ. Statistics 24, 455\u2013469 (2006)","journal-title":"J. Bus. Econ. Statistics"},{"key":"9078_CR18","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1111\/j.1467-9868.2005.00517.x","volume":"67","author":"H. Tsai","year":"2005","unstructured":"Tsai, H., Chan, K.S.: A note on non-negative continuous-time processes. J. R. Stat. Soc. Ser. B 67, 589\u2013597 (2005)","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"9078_CR19","unstructured":"Tsai, H., Chan, K.S.: A Note on the Non-negativity of Continuous-time ARMA and GARCH Processes. Technical Report No. 359, Department of Statistics and Actuarial Science, The University of Iowa (2006). Downloadable from http:\/\/www.stat.uiowa.edu\/techrep\/tr359.pdf"}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-008-9078-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11222-008-9078-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-008-9078-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T10:10:49Z","timestamp":1559383849000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11222-008-9078-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,7,4]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,6]]}},"alternative-id":["9078"],"URL":"https:\/\/doi.org\/10.1007\/s11222-008-9078-7","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,7,4]]}}}