论文标题
修改后的Galton-Watson工艺在替代后代机制下具有移民
Modified Galton-Watson processes with immigration under an alternative offspring mechanism
论文作者
论文摘要
我们提出了一种新颖的计数时间序列模型，替代了经典的Galton-Watson进程（GWI）和Bernoulli后代。开发了一种新的后代机制，并探索了其特性。这种称为几何变薄算子的新型机制用于定义一类改良的GWI（MGWI）过程，该过程诱导了模型的某些非线性。我们表明，与文献中常见的线性案例相比，这种非线性可以在预测方面产生更好的结果。我们探索MGWI流程的固定版本和非平稳版本。解决了模型参数的推断，并通过蒙特卡洛模拟研究了估计器的有限样本行为。分析了两个真实的数据集，以说明固定案例和非平稳情况，以及我们方法对现有线性方法诱导的非线性的增益。还提出了几何稀疏操作员和相关的MGWI过程的概括，并激发了处理零泄漏或零泄漏的计数时间序列数据的动机。
We propose a novel class of count time series models alternative to the classic Galton-Watson process with immigration (GWI) and Bernoulli offspring. A new offspring mechanism is developed and its properties are explored. This novel mechanism, called geometric thinning operator, is used to define a class of modified GWI (MGWI) processes, which induces a certain non-linearity to the models. We show that this non-linearity can produce better results in terms of prediction when compared to the linear case commonly considered in the literature. We explore both stationary and non-stationary versions of our MGWI processes. Inference on the model parameters is addressed and the finite-sample behavior of the estimators investigated through Monte Carlo simulations. Two real data sets are analyzed to illustrate the stationary and non-stationary cases and the gain of the non-linearity induced for our method over the existing linear methods. A generalization of the geometric thinning operator and an associated MGWI process are also proposed and motivated for dealing with zero-inflated or zero-deflated count time series data.
