Continuous autoregressive moving average models: From discrete AR to Lévy-driven CARMA models

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dc.contributor.authorArı, Yakup
dc.date.accessioned2026-01-24T12:20:57Z
dc.date.available2026-01-24T12:20:57Z
dc.date.issued2021
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractThe financial time series have a high frequency and the difference between their observations is not regular. Therefore, continuous models can be used instead of discrete-time series models. The purpose of this chapter is to define Lévy-driven continuous autoregressive moving average (CARMA) models and their applications. The CARMA model is an explicit solution to stochastic differential equations, and also, it is analogue to the discrete ARMA models. In order to form a basis for CARMA processes, the structures of discrete-time processes models are examined. Then stochastic differential equations, Lévy processes, compound Poisson processes, and variance gamma processes are defined. Finally, the parameter estimation of CARMA(2,1) is discussed as an example. The most common method for the parameter estimation of the CARMA process is the pseudo maximum likelihood estimation (PMLE) method by mapping the ARMA coefficients to the corresponding estimates of the CARMA coefficients. Furthermore, a simulation study and a real data application are given as examples. © 2021, IGI Global.
dc.identifier.doi10.4018/978-1-7998-7701-1.ch007
dc.identifier.endpage141
dc.identifier.isbn9781799877011
dc.identifier.isbn9781799877035
dc.identifier.scopus2-s2.0-85127981771
dc.identifier.scopusqualityN/A
dc.identifier.startpage118
dc.identifier.urihttps://doi.org/10.4018/978-1-7998-7701-1.ch007
dc.identifier.urihttps://hdl.handle.net/20.500.12868/4717
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherIGI Global
dc.relation.publicationcategoryKitap Bölümü - Uluslararası
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_Scopus_20260121
dc.titleContinuous autoregressive moving average models: From discrete AR to Lévy-driven CARMA models
dc.typeBook Chapter

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