The original generalized network autoregressive models are poor for modelling count data as they are based on the additive and constant noise assumptions, which is usually inappropriate for count data. We introduce two new models (GNARI and NGNAR) for count network time series by adapting and extending existing count-valued time series models. We present results on the statistical and asymptotic properties of our new models and their estimates obtained by conditional least squares and maximum likelihood. We conduct two simulation studies that verify successful parameter estimation for both models and conduct a further study that shows, for negative network parameters, that our NGNAR model outperforms existing models and our other GNARI model in terms of predictive performance. We model a network time series constructed from COVID-positive counts for counties in New York State during 2020-22 and show that our new models perform considerably better than existing methods for this problem.

翻译：原始的广义网络自回归模型基于加性常数噪声假设，在拟合计数数据时表现不佳，这通常不适用于计数数据。我们通过调整并扩展已有的计数时间序列模型，引入了两种面向计数网络时间序列的新模型（GNARI和NGNAR）。我们给出了新模型及其通过条件最小二乘法和极大似然估计得到的参数估计的统计与渐近性质结果。通过两项模拟研究验证了两种模型的参数估计均能成功实现，并进一步发现：在负网络参数情形下，我们的NGNAR模型在预测性能上优于现有模型及我们提出的另一种GNARI模型。我们针对2020-22年纽约州各县新冠肺炎阳性病例构成的网络时间序列进行建模，结果表明新模型在该问题上的表现显著优于现有方法。