ADCINAR(1)模型的加权条件最小二乘估计

吉林大学学报(理学版) ›› 2019, Vol. 57 ›› Issue (3): 553-561.

ADCINAR(1)模型的加权条件最小二乘估计

王宇¹, 王纯杰²，张海祥^1

1. 天津大学应用数学中心, 天津 300072； 2. 长春工业大学数学与统计学院，长春 130012

收稿日期:2018-05-11 出版日期:2019-05-26 发布日期:2019-05-20
通讯作者: 张海祥 E-mail:haixiang.zhang@tju.edu.cn

Weighed Conditional Least Squares Estimation for ADCINAR(1) Model

WANG Yu¹, WANG Chunjie², ZHANG Haixiang¹

1. Center for Applied Mathematics, Tianjin University, Tianjin 300072, China;2. School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China

Received:2018-05-11 Online:2019-05-26 Published:2019-05-20
Contact: ZHANG Haixiang E-mail:haixiang.zhang@tju.edu.cn

摘要/Abstract

摘要： 用加权条件最小二乘方法, 对基于相依计数序列的一阶整值自回归模型(ADCINAR(1))进行参数估计, 给出参数估计的表达式及其渐近分布, 并推导模型的高阶矩、高阶累积量、谱密度和双谱密度. 数值模拟结果表明, 将加权条件最小二乘估计、条件最小二乘估计和YuleWalker估计进行比较, 验证了加权条件最小二乘方法的有效性.

关键词: 双谱密度, 相依计数序列, 高阶矩, 整值时间序列, 加权条件最小二乘

Abstract: Using the weighed conditional least squares method, we estimated the parameters of the firstorder integer-valued autoregressive model (ADCINAR(1)) based on dependent counting series. We gave the expression of parameter estimation
and its asymptotic distribution, and derived the higherorder moments, higherorder cumulants, spectral density and bispectral density of the model. The numerical simulation results show that the validity of weighed conditional least squares method is verified by comparing weighed conditional least squares estimation with conditional least squares estimation and YuleWalker estimation.

Key words: bispectral density, dependent counting series, higherorder moment, integervalued time series, weighed conditional least squares

中图分类号:

O212.7

王宇, 王纯杰, 张海祥. ADCINAR(1)模型的加权条件最小二乘估计[J]. 吉林大学学报(理学版), 2019, 57(3): 553-561.

WANG Yu, WANG Chunjie, ZHANG Haixiang. Weighed Conditional Least Squares Estimation for ADCINAR(1) Model[J]. Journal of Jilin University Science Edition, 2019, 57(3): 553-561.

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