Mixing properties of Skellam-GARCH processes
Statistics Theory
2020-08-14 v2 Applications
Statistics Theory
Abstract
We consider integer-valued GARCH processes, where the count variable conditioned on past values of the count and state variables follows a so-called Skellam distribution. Using arguments for contractive Markov chains we prove that the process has a unique stationary regime. Furthermore, we show asymptotic regularity (-mixing) with geometrically decaying coefficients for the count process. These probabilistic results are complemented by a statistical analysis, a few simulations as well as an application to recent COVID-19 data.
Cite
@article{arxiv.2005.12093,
title = {Mixing properties of Skellam-GARCH processes},
author = {Paul Doukhan and Naushad Mamode Khan and Michael H. Neumann},
journal= {arXiv preprint arXiv:2005.12093},
year = {2020}
}