In this paper, we introduce flexible observation-driven $\mathbb{Z}$-valued time series models constructed from mixtures of negative and non-negative components. Compared to models based on the standard Skellam distribution or on a difference of two integer-valued variables, our specification offers greater versatility. For example, it easily allows for skewness and bimodality. Furthermore, the observation of one component of the mixture makes interpretation and statistical analysis easier. We establish conditions for stationarity and mixing, and develop a mixed Poisson quasi-maximum likelihood estimator with proven asymptotic properties. A portmanteau test is proposed to diagnose residual serial dependence. The finite-sample performance of the methodology is assessed via simulation, and an empirical application on tick prices demonstrates its practical usefulness.

翻译：本文提出了一种灵活的观测驱动型$\mathbb{Z}$值时间序列模型，该模型由负值与非负值分量的混合构建而成。相较于基于标准Skellam分布或两个整数值变量差分的模型，我们的设定具有更强的通用性。例如，该模型可轻松实现偏态与双峰分布特征。此外，对混合模型中某一分量的观测使得模型解释与统计分析更为简便。我们建立了模型的平稳性与混合性条件，并开发了具有渐进性质证明的混合泊松拟极大似然估计量。提出了混成检验以诊断残差序列相关性。通过仿真实验评估了该方法在有限样本下的性能，并以报价点数据的实证应用证明了其实际效用。