دورية أكاديمية
A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes
| العنوان: | A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes |
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| المؤلفون: | Arratia, Argimiro, Cabaña, Alejandra, Cabaña, Enrique M. |
| المصدر: | SORT- Statistics and Operations Research Transactions; 2016: Vol.: 40 Núm.: 2 July-December; p. 267-302 SORT-Statistics and Operations Research Transactions; 2016: Vol.: 40 Núm.: 2 July-December; p. 267-302 |
| Publication Status: | published |
| بيانات النشر: | SORT- Statistics and Operations Research Transactions, 2016. |
| سنة النشر: | 2016 |
| مصطلحات موضوعية: | Ornstein-Uhlenbeck process, Lévy process, Continuous ARMA, stationary process, 60G10, 62M10, 62M99 60M99 |
| الوصف: | We present a construction of a family of continuous-time ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an Ornstein-Uhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We show that this family is in fact a subfamily of the well-known CARMA(p,q) processes, with several interesting advantages, including a smaller number of parameters. The resulting processes are linear combinations of Ornstein-Uhlenbeck processes all driven by the same Lévy process. This provides a straightforward computation of covariances, a state-space model representation and methods for estimating parameters. Furthermore, the discrete and equally spaced sampling of the process turns to be an ARMA(p, p−1) process. We propose methods for estimating the parameters of the iterated Ornstein-Uhlenbeck process when the noise is either driven by a Wiener or a more general Lévy process, and show simulations and applications to real data. |
| نوع الوثيقة: | article |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 2013-8830 1696-2281 |
| Relation: | https://www.raco.cat/index.php/SORT/article/view/316146/406260 |
| URL الوصول: | https://www.raco.cat/index.php/SORT/article/view/316146 |
| حقوق: | From February 2013 articles are under a Creative Commons license: CC BY-NC-ND You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work), you may not use the work for commercial purposes and you may not alter, transform, or build upon the work. |
| رقم الأكسشن: | edsrac.316146 |
| قاعدة البيانات: | RACO (Revistes Catalanes amb Accés Obert) |
| تدمد: | 20138830 16962281 |
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