Prediction in a Poisson cluster model with multiple clusterprocesses
Prediction in a Poisson cluster model with multiple clusterprocesses
复制标题
具有多个聚类过程的泊松聚类模型中的预测
DOI：
10.1080/03461238.2013.773938
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
M
中科院分区：
文献类型：
--
作者：
Matsui;M
我们考虑对Matsui & Mikosch（2010）研究的泊松聚类模型进行简单而灵活的扩展。在前一种方法中，在泊松过程的每个跳跃点只建模一个集群过程，而在每个跳跃点我们随机启动给定数量的集群过程。这种简单的扩展在预测基于过去观测的过程的未来增量时产生了额外的数学问题。然而，通过充分利用模型的泊松结构，我们推导出合理的显式预测因子表达式，这在保险应用中是至关重要的。当聚类过程为复合泊松过程时，用均方误差对预测因子进行了比较。结果得出了一个自然的结论：我们使用的信息越精细，我们得到的预测结果就越好。
We consider a simple but flexible extension of the Poisson cluster model studied in Matsui & Mikosch (2010). In the former, model only a single cluster process starts at each jump point of the Poisson process, whereas we start a randomly given number of cluster processes at each jump. This simple extension yields additional mathematical problems in prediction of future increments of the process which are based on the past observations. However, by making full use of the Poisson structure of the model, we derive reasonably explicit expressions for predictors, which is of critical importance in the insurance application. Some comparisons of predictors are also made by their mean-squared errors when the cluster process is a compound Poisson process. The result yields a natural conclusion that the finer information we use, the better predictors we obtain.