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Correlation properties of continuous-time autoregressive processes delayed by the inverse of the stable subordinator

We define the delayed Lévy-driven continuous- time autoregressive process via the inverse of the stable subordinator. We derive correlation structure for the observed non-stationary delayed Lévy-driven continuous- time autoregressive processes of order p, emphasising low orders, and we show they exhibit long-range dependence property. Dis- tributional properties are discussed as well.

Continuous-time autoregressive process, Lévy noise, Delayed stochastic process, Inverse of the stable subordinator, Mittag-Leffler function, Correlation structure

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