Recent results in the theory and applications of CARMA processes

P. Brockwell ()

Annals of the Institute of Statistical Mathematics, 2014, vol. 66, issue 4, 647-685

Abstract: Just as ARMA processes play a central role in the representation of stationary time series with discrete time parameter, $$(Y_n)_{n\in \mathbb {Z}}$$ ( Y n ) 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). Copyright The Institute of Statistical Mathematics, Tokyo 2014

Keywords: Time series; Stationary process; CARMA process; Sampled process; High-frequency sampling; Inference; Prediction (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (21)

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DOI: 10.1007/s10463-014-0468-7

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