一个斜真INAR（1）过程及其应用
A skew true INAR(1) process with application
摘要：
在过去的三十年里，整数值时间序列模型一直是许多论文中反复出现的主题，但只有少数论文涉及$\mathbb Z$（即包括负整数和正整数）上的模型。本文的目的是在具有斜离散Laplace边缘的$\mathbb Z$上引入一阶整数值自回归过程（Kozubowski and Inusah，2006）。为此，我们定义了一个新的算子，它作用于两个独立的潜在过程，类似于Freeland（2010）。我们推导了该过程的一些联合和条件的基本性质，如特征函数，矩，高阶矩和跳跃。我们的模型的参数估计，并建立其渐近正态性。我们运行一个蒙特卡罗模拟来评估这些估计的有限样本性能。为了说明我们的过程的潜力，我们将其应用到一个真实的数据集的人口增长率。
英文摘要：
Integer-valued time series models have been a recurrent theme considered in many papers in the last three decades, but only a few of them have dealt with models on $\mathbb Z$ (that is, including both negative and positive integers). Our aim in this paper is to introduce a first-order integer-valued autoregressive process on $\mathbb Z$ with skew discrete Laplace marginals (Kozubowski and Inusah, 2006). For this, we define a new operator that acts on two independent latent processes, similarly as made by Freeland (2010). We derive some joint and conditional basic properties of the proposed process such as characteristic function, moments, higher-order moments and jumps. Estimators for the parameters of our model are proposed and their asymptotic normality are established. We run a Monte Carlo simulation to evaluate the finite-sample performance of these estimators. In order to illustrate the potentiality of our process, we apply it to a real data set about population increase rates.
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