An alternative to CARMA models via iterations of Ornstein–Uhlenbeck processes

Argimiro Arratia*, Alejandra Cabaña, Enrique M. Cabaña

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review


© Springer International Publishing AG 2017. We present a new construction of continuous ARMA processes based on iterating an Ornstein–Uhlenbeck operator OU κ that maps a random variable y(t) onto OU κ y(t) = ∫ t –∞ e –κ(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.
Original languageEnglish
Pages (from-to)101-107
Number of pages7
JournalTrends in Mathematics
Publication statusPublished - 1 Jan 2017


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