ABSTRACT This paper presents a new stationary integer-valued bilinear time series model of the first order by mixing the thinning and Pegram operators. Some statistical properties of the model are obtained, involving the conditional moments, autocovariance and spectral density function. Estimation of the model parameters is discussed using the Yule-Walker and conditional least squares methods with a simulation study for evaluating the performance of those estimators. Applicability of the process is investigated using a practical count data set with comparing the model to a competitive bilinear model using some marginal distributions of innovations. Issue of forecasting data is discussed under the proposed model.

中文翻译：

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基于两个随机算子的整数值双线性时间序列模型

摘要 本文通过混合细化和 Pegram 算子，提出了一种新的一阶平稳整数值双线性时间序列模型。获得了模型的一些统计特性，包括条件矩、自协方差和谱密度函数。使用 Yule-Walker 和条件最小二乘法以及用于评估这些估计器性能的模拟研究来讨论模型参数的估计。使用实际计数数据集研究该过程的适用性，并使用一些创新的边际分布将模型与竞争双线性模型进行比较。在建议的模型下讨论了预测数据的问题。