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

摘要

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