ADCINAR(1)模型的加权条件最小二乘估计
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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.
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.
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.
引文
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[10]ZHANG Haixiang,WANG Dehui,SUN Liuquan.Regularized Estimation in GINAR(p)Process[J].Journal of the Korean Statistical Society,2017,46(4):502-517.
[11]NASTIC'A S,RISTIC'M M,MILETIC'ILIC'A V.A Geometric Time-Series Model with an Alternative Dependent Bernoulli Counting Series[J].Comunications in Statistic:Theory and Methods,2017,46(2):770-785.
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[13]HALL P,HEYDE C C.Martingale Limit Theory and Its Application[M].New York:Academic Press,1980.
[2]DU Jinguan,LI Yuan.The Integer-Valued Autoregressive(INAR(p))Model[J].Journal of Time Series Analysis,1991,12(2):129-142.
[3]ZHENG Haitao,BASAWA I V,DATTA S.First-Order Random Coefficient Integer-Valued Autoregressive Processes[J].Journal of Statistical Planning and Inference,2007,137(1):212-229.
[4]RISTIC'M M,BAKOUCH H S,NASTIC'A S.A New Geometric First-Order Integer-Valued Autoregressive(NGINAR(1))Process[J].Journal of Statistical Planning and Inference,2009,139(7):2218-2226.
[5]BAKOUCH H S,RISTIC'M M.Zero Truncated Poisson Integer-Valued AR(1)Model[J].Metrika,2010,72(2):265-280.
[6]ZHANG Haixiang,WANG Dehui,ZHU Fukang.Inference for INAR(p)Processes with Signed Generalized Power Series Thinning Operator[J].Journal of Statistical Planning and Inference,2010,140(3):667-683.
[7]ZHENG Haitao,BASAWA I V,DATTA S.Inference for pth-Order Random Coefficient Integer-Valued Autoregressive Processes[J].Journal of Time Series Analysis,2006,27(3):411-440.
[8]DROST F C,AKKER R V,WERKER B J M.Efficient Estimation of Auto-regression Parameters and Innovation Distributions for Semiparametric Integer-Valued AR(p)Models[J].Journal of the Royal Statistical Society:Series B,2009,71(2):467-485.
[9]ZHANG Haixiang,WANG Dehui,ZHU Fukang.Empirical Likelihood Inference for Random Coefficient INAR(p)Process[J].Journal of Time Series Analysis,2011,32(3):195-203.
[10]ZHANG Haixiang,WANG Dehui,SUN Liuquan.Regularized Estimation in GINAR(p)Process[J].Journal of the Korean Statistical Society,2017,46(4):502-517.
[11]NASTIC'A S,RISTIC'M M,MILETIC'ILIC'A V.A Geometric Time-Series Model with an Alternative Dependent Bernoulli Counting Series[J].Comunications in Statistic:Theory and Methods,2017,46(2):770-785.
[12]BILLINGSLEY P.Statistical Inference for Markov Processes[M].Chicago:University of Chicago Press,1961:3-6.
[13]HALL P,HEYDE C C.Martingale Limit Theory and Its Application[M].New York:Academic Press,1980.