论文标题
具有灵活的边际和创新分布的整数值自回归过程
Integer-valued autoregressive process with flexible marginal and innovation distributions
论文作者
论文摘要
整数自动回归（INAR）过程通常是通过指定创新和操作员来定义的，这通常会导致难以推导该过程的边际特性。在许多实际情况下，一个主要的建模限制是很难证明操作员的选择是合理的。为了克服这些缺点，我们提出了一种新的灵活方法来构建INAR模型：我们预先指定了边际和创新分布。因此，操作员是指定所需的边际和创新分布的结果。我们的新INAR模型具有边际和创新的几何分布，是经典泊松Inar模型的直接替代方法。我们提出的过程具有有趣的随机属性，例如MA（$ \ infty $）表示，时间可逆性和过渡概率的封闭形式$ h $ steps $ h $ steps，从而可以进行连贯的预测。我们使用建议的方法与现有的INAR和INGARCH模型进行了比较，分析了皮肤病变的时间序列计数。我们的模型更加坚持数据和更好的预测性能。
INteger Auto-Regressive (INAR) processes are usually defined by specifying the innovations and the operator, which often leads to difficulties in deriving marginal properties of the process. In many practical situations, a major modeling limitation is that it is difficult to justify the choice of the operator. To overcome these drawbacks, we propose a new flexible approach to build an INAR model: we pre-specify the marginal and innovation distributions. Hence, the operator is a consequence of specifying the desired marginal and innovation distributions. Our new INAR model has both marginal and innovations geometric distributed, being a direct alternative to the classical Poisson INAR model. Our proposed process has interesting stochastic properties such as an MA($\infty$) representation, time-reversibility, and closed-forms for the transition probabilities $h$-steps ahead, allowing for coherent forecasting. We analyze time-series counts of skin lesions using our proposed approach, comparing it with existing INAR and INGARCH models. Our model gives more adherence to the data and better forecasting performance.
