Multivariate stochastic delay differential equations and CAR representations of CARMA processes

Basse-O’Connor, Andreas, Mikkel Slot Nielsen, Jan Pedersen and Victor Rohde

Stochastic Processes and their Applications, 2019, vol. 129, issue 10, 4119-4143

Abstract: In this study we show how to represent a continuous time autoregressive moving average (CARMA) as a higher order stochastic delay differential equation, which may be thought of as a CAR(∞) representation. Furthermore, we show how the CAR(∞) representation gives rise to a prediction formula for CARMA processes. To be used in the above mentioned results we develop a general theory for multivariate stochastic delay differential equations, which will be of independent interest, and which will have particular focus on existence, uniqueness and representations.

Keywords: Multivariate stochastic delay differential equations; Multivariate Ornstein–Uhlenbeck processes; CARMA processes; FICARMA processes; MCARMA processes; Noise recovery; Prediction; Long memory (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2018.11.011

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