Correlation properties of continuous-time autoregressive processes delayed by the inverse of the stable subordinator |
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| Authors: | Nikolai N Leonenko Ivan Papić |
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| Institution: | 1. School of Mathematics, Cardiff University, Cardiff, UK;2. LeonenkoN@cardiff.ac.uk;4. Department of Mathematics, J. J. Strossmayer University of Osijek, Osijek, Croatia |
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| Abstract: | AbstractWe 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, emphasizing low orders, and we show they exhibit long-range dependence property. Distributional properties are discussed as well. |
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| Keywords: | Continuous-time autoregressive process Lévy noise delayed stochastic process inverse of the stable subordinator Mittag-Leffler function correlation structure |
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