一阶随机系数整数值二项自回归模型的参数估计
Parameter Estimation for the First-Order Random Coefficient Integer-Valued Binomial Autoregressive Model
摘要: 本文系统研究了一阶随机系数整数值二项自回归模型，在参数估计方面，分别构建了模型参数的条件最小二乘估计量与拟似然估计量，并基于最小二乘估计量进一步引入经验似然方法，构造了具有辅助信息的最大经验似然估计量。最后，通过仿真实验，在不同样本量、参数设置与数据生成机制下，综合比较了上述估计方法的有限样本性能，为离散时间序列数据的建模提供了更丰富的估计工具与理论参考。
Abstract: This paper systematically studies the first-order random coefficient integer-valued binomial autoregressive model. In parameter estimation, it constructs the conditional least squares estimator and the quasi-likelihood estimator for the model parameters, and further introduces an empirical likelihood method based on the least squares estimator to construct the maximum empirical likelihood estimator with auxiliary information. Finally, through simulation experiments under different sample sizes, parameter settings, and data generating mechanisms, it comprehensively compares the finite-sample performance of the above estimation methods, providing more estimation tools and theoretical references for modeling discrete time series data.
文章引用：陈志非, 卢飞龙. 一阶随机系数整数值二项自回归模型的参数估计[J]. 应用数学进展, 2026, 15(2): 281-292. https://doi.org/10.12677/aam.2026.152069

参考文献

[1] Mckenzie, E. (1988) Some ARMA Models for Dependent Sequences of Poisson Counts. Advances in Applied Probability, 20, 822-835. [Google Scholar] [CrossRef] 
[2] Al‐Osh, M.A. and Alzaid, A.A. (1987) First-Order Integer-Valued Autoregressive (INAR(1)) Process. Journal of Time Series Analysis, 8, 261-275. [Google Scholar] [CrossRef] 
[3] Steutel, F.W. and van Harn, K. (1979) Discrete Analogues of Self-Decomposability and Stability. The Annals of Probability, 7, 893-899. [Google Scholar] [CrossRef] 
[4] Weiß, C.H. and Pollett, P.K. (2013) Binomial Autoregressive Processes with Density‐Dependent Thinning. Journal of Time Series Analysis, 35, 115-132. [Google Scholar] [CrossRef] 
[5] Weiß, C.H. and Kim, H. (2012) Parameter Estimation for Binomial AR(1) Models with Applications in Finance and Industry. Statistical Papers, 54, 563-590. [Google Scholar] [CrossRef] 
[6] Zheng, H., Basawa, I.V. and Datta, S. (2007) First-order Random Coefficient Integer-Valued Autoregressive Processes. Journal of Statistical Planning and Inference, 137, 212-229. [Google Scholar] [CrossRef] 
[7] Owen, A.B. (1988) Empirical Likelihood Ratio Confidence Intervals for a Single Functional. Biometrika, 75, 237-249. [Google Scholar] [CrossRef] 
[8] Owen, A. (1990) Empirical Likelihood Ratio Confidence Regions. The Annals of Statistics, 18, 90-120. [Google Scholar] [CrossRef] 
[9] Owen, A. (1991) Empirical Likelihood for Linear Models. The Annals of Statistics, 19, 1725-1747. [Google Scholar] [CrossRef] 
[10] Qin, J. and Lawless, J. (1994) Empirical Likelihood and General Estimating Equations. The Annals of Statistics, 22, 300-325. [Google Scholar] [CrossRef] 
[11] Chuang, C.S. and Chan, N.H. (2002) Empirical Likelihood for Autoregressive Models, with Applications to Unstable Time Series. Statistica Sinica, 12, 387-407.
[12] Chan, N.H. and Ling, S. (2006) Empirical Likelihood for GARCH Models. Econometric Theory, 22, 403-428. [Google Scholar] [CrossRef] 
[13] Zhang, R. and Wang, D. (2022) Bayesian Empirical Likelihood Inference for the Generalized Binomial AR(1) Model. Journal of the Korean Statistical Society, 51, 977-1004. [Google Scholar] [CrossRef] 
[14] Yang, K., Wang, D. and Li, H. (2017) Threshold Autoregression Analysis for Finite-Range Time Series of Counts with an Application on Measles Data. Journal of Statistical Computation and Simulation, 88, 597-614. [Google Scholar] [CrossRef] 
[15] Weiß, C.H. (2009) A New Class of Autoregressive Models for Time Series of Binomial Counts. Communications in Statistic—Theory and Methods, 38, 447-460. [Google Scholar] [CrossRef] 
[16] Ma, T. and Wang, D. (2023) First-Order Random Coefficient Binomial AR Process with Dependent Counting Series. Communications in Statistics—Simulation and Computation, 54, 71-90. [Google Scholar] [CrossRef] 
[17] Weiß, C.H. and Kim, H.Y. (2011) Binomial AR(1) Processes: Moments, Cumulants, and Estimation. Statistics, 45, 279-295.
[18] Klimko, L.A. and Nelson, P.I. (1978) On Conditional Least Squares Estimation for Stochastic Processes. The Annals of Statistics, 6, 629-642. [Google Scholar] [CrossRef] 
[19] Lu, F. and Wang, D. (2021) A New Estimation for INAR(1) Process with Poisson Distribution. Computational Statistics, 37, 1185-1201. [Google Scholar] [CrossRef] 
[20] Mykland, P.A. (1995) Dual Likelihood. The Annals of Statistics, 23, 396-421.

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