Recent results in the theory and applications of CARMA processes

Just as ARMA processes play a central role in the representation of stationary time series with discrete time parameter, $$(Y_n)_{n\in \mathbb {Z}}$$(Yn)n∈Z, CARMA processes play an analogous role in the representation of stationary time series with continuous time parameter, $$(Y(t))_{t\in \mathbb {R}}$$(Y(t))t∈R. Lévy-driven CARMA processes permit the modelling of heavy-tailed and asymmetric time series and incorporate both distributional and sample-path information. In this article we provide a review of the basic theory and applications, emphasizing developments which have occurred since the earlier review in Brockwell (2001a, In D. N. Shanbhag and C. R. Rao (Eds.), Handbook of Statistics 19; Stochastic Processes: Theory and Methods (pp. 249–276), Amsterdam: Elsevier).

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