Hierarchical Count Echo State Network Models with Application to Graduate Student Enrollments

TL;DR

This paper introduces hierarchical count echo state networks as a novel approach for modeling correlated count data, demonstrating their effectiveness on a large dataset of graduate student enrollments and outperforming traditional models.

Contribution

It develops Poisson and negative binomial echo state network models for count data, providing a new flexible alternative to Poisson autoregressive models with hierarchical extensions.

Findings

Hierarchical negative binomial echo state network outperforms other models in forecasting accuracy.

The proposed models effectively handle overdispersion in count data.

Application to graduate student enrollments demonstrates practical utility.

Abstract

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.