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

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.

Nonlinear Time Series Classification Using Bispectrum-based Deep Convolutional Neural Networks

Time series classification using novel techniques has experienced a recent resurgence and growing interest from statisticians, subject-domain scientists, and decision makers in business and industry. This is primarily due to the ever increasing amount of big and complex data produced as a result of technological advances. A motivating example is that of Google trends data, which exhibit highly nonlinear behavior. Although a rich literature exists for addressing this problem, existing approaches mostly rely on first and second order properties of the time series, since they typically assume linearity of the underlying process. Often, these are inadequate for effective classification of nonlinear time series data such as Google Trends data. Given these methodological deficiencies and the abundance of nonlinear time series that persist among real-world phenomena, we introduce an approach that merges higher order spectral analysis (HOSA) with deep convolutional neural networks (CNNs) for classifying time series. The effectiveness of our approach is illustrated using simulated data and two motivating industry examples that involve Google trends data and electronic device energy consumption data.