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Parameters Estimate and Bootstrap Confidence Intervals of Generalized Exponential Family ARMA Models

Abstract

本文针对广义指数族ARMA模型,分为连续型指数族和离散型指数族两种情况讨论模型的参数估计,并运用不同的Bootstrap方法构造参数的置信区间和置信带.两种情况均采用Scoring算法进行模型的参数估计,并分别得到Scoring算法中两个模型方向向量的计算公式.对于连续型情况,运用WildBootstrap构造参数的置信区间和置信带,并将其结果与传统的残差Bootstrap进行比较,得到WildBootstrap更快更精确的结论;对于离散型情况,运用分块移动Bootstrap构造参数的置信区间,这种方法更加实用,收敛速度快,并得到较为满意的结果.The objective of this paper is to estimate the parameters of generalized exponential family ARMA models and construct the confidence intervals of the parameters. In this paper we divided the problem into continuous type situation and discrete type situation. Under both situations,we use Fisher Scoring algorithm to estimate the parameters and gain the formula of direction vectors in the algorithm.U...学位:理学硕士院系专业:数学科学学院数学与应用数学系_概率论与数理统计学号:20032303

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