基于NGINAR(p)模型的贝叶斯非参数预测

Bayesian Nonparametric Forecasting for NGINAR(p) Models

摘要: 本文将Bisaglia和Canale (2016)提出的贝叶斯非参数预测框架从INAR模型拓展至基于负二项稀疏算子的广义p阶整数值自回归模型(NGINAR(p))。该拓展利用负二项稀疏算子刻画高阶依赖结构与过度离散特征，并采用舍入高斯混合先验对创新项分布进行非参数建模，从而灵活捕捉计数数据中普遍存在的多峰、偏态等复杂分布形态。针对高阶模型的结构复杂性，构建了基于数据增强的Gibbs采样算法，实现自回归系数与创新项分布的联合后验推断，并直接获得整数值的h步向前预测分布。模拟研究与中国某地区月度总云量数据的实证分析表明，该方法在不同样本量、自回归系数及创新项分布设定下均表现出良好的预测精度与稳定性，在处理高阶复杂计数时间序列时具有显著的适应性与有效性。

Abstract: This paper extends the Bayesian nonparametric prediction framework proposed by Bisaglia and Canale (2016) from the INAR model to the generalized p-order integer-valued autoregressive model based on the negative binomial thinning operator (NGINAR(p)). This extension utilizes the negative binomial thinning operator to describe the high-order dependency structure and overdispersion characteristics, and employs a rounded Gaussian mixture prior for nonparametric modeling of the innovation term distribution, thereby flexibly capturing complex distributional forms such as multimodality and skewness commonly found in count data. To address the structural complexity of high-order models, a data augmentation-based Gibbs sampling algorithm is constructed to jointly infer the posterior distribution of the autoregressive coefficients and the innovation term distribution, and directly obtain the h-step ahead predictive distribution of integer values. Simulation studies and empirical analysis of monthly total cloud cover data from a certain region in China demonstrate that this method exhibits excellent prediction accuracy and stability under different sample sizes, autoregressive coefficient settings, and innovation term distribution assumptions, and shows significant adaptability and effectiveness in handling high-order complex count time series.