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.

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关于两类反射自回归过程

我们介绍了两类反射自回归过程，INGAR+和 GAR+. 在这里，因加+可以看作是 INAR(1) 的对应物，通过一般细化和反射来保持过程非负；加尔+以类似的方式与 AR(1) 相关。INGAR的两个过程+和 GAR+显示通过对偶关系连接。我们继续详细分析 INGAR 的时间相关和静止行为+过程，然后利用对偶关系来获得 GAR 的时间相关和平稳的行为+过程。