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On two classes of reflected autoregressive processes. (English) Zbl 1444.62098

Summary: We introduce two general classes of reflected autoregressive processes, \(\mathrm{INGAR}^+\) and \(\mathrm{GAR}^+\). Here, \(\mathrm{INGAR}^+\) can be seen as the counterpart of INAR(1) with general thinning and reflection being imposed to keep the process non-negative; \(\mathrm{GAR}^+\) relates to AR(1) in an analogous manner. The two processes \(\mathrm{INGAR}^+\) and \(\mathrm{GAR}^+\) 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 \(\mathrm{INGAR}^+\) process, and then exploit the duality relation to obtain the time-dependent and stationary behavior of the \(\mathrm{GAR}^+\) process.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
60K25 Queueing theory (aspects of probability theory)

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