On two classes of reflected autoregressive processes. (June 2020) - Boxma, Onno; Löpker, Andreas; Mandjes, Michel
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.