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Continuous Autoregressive Moving Average Models: From Discrete AR to Lévy-Driven CARMA Models

Continuous Autoregressive Moving Average Models: From Discrete AR to Lévy-Driven CARMA Models

Yakup Ari
Copyright: © 2021 |Pages: 24
ISBN13: 9781799877011|ISBN10: 1799877019|ISBN13 Softcover: 9781799877028|EISBN13: 9781799877035
DOI: 10.4018/978-1-7998-7701-1.ch007
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MLA

Ari, Yakup. "Continuous Autoregressive Moving Average Models: From Discrete AR to Lévy-Driven CARMA Models." Methodologies and Applications of Computational Statistics for Machine Intelligence, edited by Debabrata Samanta, et al., IGI Global, 2021, pp. 118-141. https://doi.org/10.4018/978-1-7998-7701-1.ch007

APA

Ari, Y. (2021). Continuous Autoregressive Moving Average Models: From Discrete AR to Lévy-Driven CARMA Models. In D. Samanta, R. Rao Althar, S. Pramanik, & S. Dutta (Eds.), Methodologies and Applications of Computational Statistics for Machine Intelligence (pp. 118-141). IGI Global. https://doi.org/10.4018/978-1-7998-7701-1.ch007

Chicago

Ari, Yakup. "Continuous Autoregressive Moving Average Models: From Discrete AR to Lévy-Driven CARMA Models." In Methodologies and Applications of Computational Statistics for Machine Intelligence, edited by Debabrata Samanta, et al., 118-141. Hershey, PA: IGI Global, 2021. https://doi.org/10.4018/978-1-7998-7701-1.ch007

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Abstract

The 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.

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