用于整数值自回归模型的符号矩阵稀疏化与投影估计
Signed Matrix Thinning and Projection Estimation for Integer-Valued Autoregressive Models
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中文总结 AI 辅助
本文针对MINAR模型无法处理负值的缺陷，提出Z-MINAR模型，通过符号矩阵稀疏化算子和扩展泊松分布实现正负整数处理，经模拟和实证验证其估计精度等性能优于基准模型。
中文摘要 AI 辅助
整数值时间序列广泛存在于金融、经济学和流行病学等领域。随着这些领域的时空数据结构日益复杂且高维，矩阵整数值自回归（MINAR）模型可有效捕捉行-列交叉相关性以降低维度，但它根本无法容纳负值，这是分析现实中差分数据或金融分笔波动的关键缺陷。为弥合这一理论与实践差距，本文提出Z-MINAR模型，这是一种定义在完整整数域（Z）上的新型矩阵自回归框架。通过首创符号矩阵稀疏化算子，并利用扩展泊松分布处理新息，Z-MINAR模型巧妙地处理正整数和负整数，同时严格保留矩阵数据固有的关键拓扑交互作用。此外，本文采用基于投影的条件最小二乘估计方法，并严格证明了该模型的平稳性、因果性和渐近正态性。大量模拟结果表明，与现有基准模型相比，Z-MINAR具有更优的估计精度、稳健性和适应性。最后，聚焦于不同城市区域犯罪计数变化的实证应用，证实了该模型在揭示Z值矩阵时间序列中动态时空依赖结构方面的实际效用。
英文摘要
Integer-valued time series are ubiquitous in fields such as finance, economics, and epidemiology. As spatiotemporal data structures in these domains grow increasingly complex and high-dimensional, the matrix integer-valued autoregressive (MINAR) model efficiently captures row-column cross-correlations to reduce dimensionality. However, it fundamentally fails to accommodate negative values, which is a critical flaw for analyzing real-world differenced data or financial tick fluctuations. To bridge this theoretical and practical gap, this paper introduces the Z-MINAR model, a novel matrix autoregressive framework defined on the full integer domain (Z). By pioneering a signed matrix thinning operator and utilizing an extended poisson distribution for the innovations, the Z-MINAR model elegantly handles both positive and negative integers while strictly preserving the crucial topological interactions inherent in matrix data. Furthermore, we employ a projection-based conditional least squares estimation procedure and rigorously establish the model's stationarity, causality, and asymptotic normality. Extensive simulations demonstrate the superior estimation accuracy, robustness, and adaptability of Z-MINAR over existing benchmark models. Finally, an empirical application focusing on crime count variations across different urban regions confirms the model's practical efficacy in uncovering dynamic spatiotemporal dependence structures in Z-valued matrix time series.
