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Published in:
2017 | OriginalPaper | Chapter
An Alternative to CARMA Models via Iterations of Ornstein–Uhlenbeck Processes
Authors : Argimiro Arratia, Alejandra Cabaña, Enrique M. Cabaña
Published in: Extended Abstracts Summer 2015
Publisher: Springer International Publishing
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Abstract
We present a new construction of continuous ARMA processes based on iterating an Ornstein–Uhlenbeck operator \(\mathcal{O}\mathcal{U}_{\kappa }\) that maps a random variable y(t) onto \(\mathcal{O}\mathcal{U}_{\kappa }y(t) =\int _{ -\infty }^{t}\mathrm{e}^{-\kappa (t-s)}dy(s)\). This construction resembles the procedure to build an AR( p) from an AR(1) and derives in a parsimonious model for continuous autoregression, with fewer parameters to compute than the known CARMA obtained as a solution of a system of stochastic differential equations. We show properties of this operator, give state space representation of the iterated Ornstein–Uhlenbeck process and show how to estimate the parameters of the model.