On two classes of reflected autoregressive processes
Onno Boxma, Andreas H. Löpker, Michel Mandjes · Journal of Applied Probability · 2020
Abstract We introduce two general classes of reflected autoregressive processes, INGAR+and GAR+. Here, INGAR+can be seen as the counterpart of INAR(1) with general thinning and reflection being imposed to keep the process non-negative; GAR+relates to AR(1) in an analogous manner. The two processes INGAR+and GAR+are shown to be connected via a duality relation. We proceed by presenting a detailed analysis of the time-dependent and stationary behavior of the INGAR+process, and then exploit the duality relation to obtain the time-dependent and stationary behavior of the GAR+process.