关键词: 整数值时间序列, 二项分布, AR(1)模型, 动态系数, 平稳性, 遍历性

Abstract: The Binomial AR(1) model defined with thinning operators is widely used for modeling integer-valued time series with finite range. The thinning probabilities are constant parameters which do not change with time. In fact, they may be affected by environmental factors, or to some extent, change with the change of the observations. The nonrandom restriction of the thinning probabilities is removed in the Binomial AR(1) model, and a kind of first-order binomial integer-valued autoregressive model with observation dependent dynamic coefficients is considered . The strict stationary and ergodicity of the process are showed. Three estimation methods of the parameters are discussed : conditional least square estimation, conditional maximum likelihood estimation and maximum empirical likelihood estimation. The consistency and asymptotic normality of the estimators are proved. A real data example is also given.

Key words: integer-valued time series, binomial distribution, AR(1) model, dynamic coefficients, stationarity, ergodicity