Academic Journal
A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes
| Title: | A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes |
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| Authors: | Arratia Quesada, Argimiro Alejandro, Cabaña, Alejandra, Cabaña, Enrique M. |
| Contributors: | Universitat Politècnica de Catalunya. Departament de Ciències de la Computació, Universitat Politècnica de Catalunya. LARCA - Laboratori d'Algorísmia Relacional, Complexitat i Aprenentatge |
| Source: | Recercat. Dipósit de la Recerca de Catalunya instname Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) SORT-Statistics and Operations Research Transactions; 2016: Vol.: 40 Núm.: 2 July-December; p. 267-302 oai:raco.cat:article/316146 Repositori Institucional de la Universitat Rovira i Virgili Universitat Rovira i virgili (URV) |
| Publisher Information: | Institut d'Estadística de Catalunya, 2016. |
| Publication Year: | 2016 |
| Subject Terms: | Àrees temàtiques de la UPC::Matemàtiques i estadística, Lévy process, Classificació AMS::62 Statistics::62N Survival analysis and censored data, Matemàtiques i estadística [Àrees temàtiques de la UPC], Processos estocàstics, 62 Statistics::62G Nonparametric inference [Classificació AMS], Lévy, Continuous arma, Ornstein-Uhlenbeck process, Lévy process, Continuous ARMA, stationary process, Stochastic processes, Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica, Matemàtiques i estadística::Estadística matemàtica [Àrees temàtiques de la UPC], Lévy processes, 60G10, 62M10, 62M99 60M99, Stationary process, Processos de, Classificació AMS::62 Statistics::62G Nonparametric inference, Lévy, Processos de, Ornstein-Uhlenbeck process, 62 Statistics::62N Survival analysis and censored data [Classificació AMS], stationary process, Continuous ARMA |
| Description: | 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 L´evy 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. |
| Document Type: | Article Other literature type |
| File Description: | application/pdf |
| DOI: | 10.2436/20.8080.02.44 |
| Access URL: | http://hdl.handle.net/2117/102108 https://ddd.uab.cat/record/168850 http://hdl.handle.net/20.500.11797/RP2448 https://hdl.handle.net/20.500.11797/RP2448 https://hdl.handle.net/2117/112746 http://hdl.handle.net/2117/112746 https://ddd.uab.cat/record/168850 https://dialnet.unirioja.es/servlet/articulo?codigo=5793820 https://upcommons.upc.edu/bitstream/2117/102108/1/ArratiaSORT2016.pdf https://ddd.uab.cat/pub/sort/sort_a2016m7-12v40n2/sort_a2016m7-12v40n2p267.pdf https://upcommons.upc.edu/handle/2117/112746 http://www.raco.cat/index.php/SORT/article/view/316146 |
| Rights: | CC BY NC ND |
| Accession Number: | edsair.dedup.wf.002..d4a2dcfe59e9f49a2e2ae6e8f26626e5 |
| Database: | OpenAIRE |
| DOI: | 10.2436/20.8080.02.44 |
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