On two classes of reflected autoregressive processes. (June 2020)

• Record Type: Journal Article
• Authors: Boxma, Onno; Löpker, Andreas; Mandjes, Michel
• Is Part Of: Journal of applied probability. Volume 57:Number 2(2020)
• Page Start: 657
• Page End: 678
• Publication Date: 2020-06
• Subjects: INAR(1), -- AR(1), -- autoregressive processes, -- reflection, -- generating functions, -- time-dependent behavior, -- stationarity; 60K10, -- 62M10, -- 60K25; 519.2
• DOI: 10.1017/jpr.2020.6
• Languages: English
• ISSNs: 0021-9002

Abstract

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.