Additive Matrix Integer-Valued Autoregressive Model
加性矩阵整数值自回归模型AI 解读 ↓
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加性矩阵整数值自回归模型
- 研究问题
- 对于具有行列依赖的矩阵计数时间序列，如何分别表达行效应、列效应和滞后动态，并提高参数解释性与预测能力？
- 方法与思路
- 作者提出 Add-MINAR，以加性结构分解矩阵响应，并构造投影估计与迭代条件最小二乘估计，研究其一致性和渐近正态性。
- 材料陈述的贡献
- 摘要称模型改善了结构解释与灵活性；模拟中迭代估计通常表现更好，芝加哥犯罪数据应用展示了相对基准的拟合和预测优势。
- 阅读关注点
- 应核对加性分解与整数值生成机制、参数识别及稳定性条件，并检查模拟场景、基准设定和样本外预测比较是否公平。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未给出渐近条件及性能数值，所述优势不能外推至所有矩阵计数序列。
原文摘要
Contemporary data-driven and technology-integrated era, various matrix-valued integer-valued time series, such as cross-regional crime statistics, multi-category sales records, and network traffic matrices, exhibit high dimensionality, complex structures, and strong row-column intertwined dependencies. Although the existing matrix integer-valued autoregressive (MINAR) model provides a framework that directly handles matrix data and captures bidirectional row-column dependencies, it suffers from limited interpretability and inflexible structural representation, as its parameters often lack clear empirical meaning and the model cannot separately distinguish the effects arising from rows, columns, and lagged dynamics. To overcome these drawbacks, this paper proposes the additive matrix integer-valued autoregressive (Add-MINAR) model. By introducing an additive structure that explicitly decomposes the matrix response into row effects, column effects, and lagged effects, the proposed model not only preserves the matrix-valued nature but also significantly enhances parameter interpretability and structural flexibility. Two estimation methods, namely projection estimation and iterative conditional least squares estimation, are developed for parameter identification and inference, and their asymptotic properties, including consistency and asymptotic normality, are rigorously established. Simulation results show that the iterative conditional least squares estimator generally outperforms the projection estimator in most scenarios. Empirical analysis of Chicago crime data further demonstrates that the Add-MINAR model achieves superior in-sample fitting and out-of-sample forecasting performance compared to benchmark models such as MINAR, making it particularly suitable for practical applications with explicit row-column interaction features.