一阶时变随机系数整数值时间序列模型研究

Research on First-Order Time-Varying Random Coefficient Model for Integer-Valued Time Series via the Poisson Thinning Operator

整数值时间序列数据通常来源于由不同的稀疏算子及可变参数构成的数据生成过程.鉴于此,文章提出了一个由泊松稀疏算子和时变随机系数构成的一阶非负整数值自回归过程.文章推导了这个随机过程的矩条件,证明了这个过程的遍历性和平稳性.随后文章就这个过程提出了三种估计方法,并且应用蒙特卡罗模拟验证了这些估计方法的性能.最后,文章将所提出的模型和方法应用于上海证券交易所数据,塞浦路斯新冠疫情数据以及全球重大地震频次数据,取得了令人满意的效果.

In many instances,integer-valued time series are derived from data generating processes that involve varying parameters and different thinning operators.In this paper,we introduce a first-order non-negative integer-valued autoregressive process,combining the Poisson thinning operator with a time-varying random coefficient.We derive the moment condition,stationarity,and ergodicity of this process.Subsequently,we present three estimation methods.To evaluate these methods'performance,we employ Monte Carlo simulation results.Additionally,we demonstrate the proposed method's utility through an analysis of data from the Shanghai Stock Exchange,COVID-19 data from Cyprus,and significant annual earthquakes and satisfactory results are obtained.