Poisson autoregressive count models have evolved into a time series staple for correlated count data. This paper proposes an alternative to Poisson autoregressions: count echo state networks. Echo state networks can be statistically analyzed in frequentist manners via optimizing penalized likelihoods, or in Bayesian manners via MCMC sampling. This paper develops Poisson echo state techniques for count data and applies them to a massive count data set containing the number of graduate students from 1,758 United States universities during the years 1972-2021 inclusive. Negative binomial models are also implemented to better handle overdispersion in the counts. Performance of the proposed models are compared via their forecasting performance as judged by several methods. In the end, a hierarchical negative binomial based echo state network is judged as the superior model.

翻译：泊松自回归计数模型已发展成为处理相关计数数据的时间序列标准方法。本文提出了一种替代泊松自回归的模型：计数回声状态网络。回声状态网络可通过优化惩罚似然函数进行频率统计推断，或通过MCMC采样进行贝叶斯分析。本文针对计数数据开发了泊松回声状态技术，并将其应用于一个包含1972至2021年间美国1,758所大学研究生数量的海量计数数据集。同时实现了负二项式模型以更好地处理计数中的过度离散问题。通过多种评估方法比较了所提出模型的预测性能。最终，基于分层负二项式的回声状态网络被判定为最优模型。