Scaling limit of heavy tailed nearly unstable INAR () processes and rough fractional diffusions

In this paper, we investigated the scaling limit of heavy tailed unstable INAR () processes where the ¹ norm of the kernel vector is close to 1 and have power law tail of the form n^- (1+), with (12, 1). The result is in contrast to the continuous-time heavy tailed unstable Hawkes processes and light-tailed INAR (p) processes. We show that the discrete-time scaling limit also has long-memory property and can also be seen as an integrated fractional Cox-Ingersoll-Ross process.