Softplus and Neural Architectures for Enhanced Negative Binomial INGARCH Modeling

TL;DR

This paper introduces novel neural network-based models for count time series forecasting, specifically the sp NB-INGARCH and neu-NB-INGARCH, demonstrating their theoretical properties and practical effectiveness through simulations and healthcare data analysis.

Contribution

It presents the first Softplus negative binomial INGARCH model with established stationarity and extends it with a neural network version for improved prediction in non-stationary count data.

Findings

The sp NB-INGARCH model is effective in simulation studies.

The neu-NB-INGARCH model improves predictive accuracy on healthcare data.

The models accommodate moderate non-stationarity in count time series.

Abstract

The study addresses a significant gap in the literature by introducing the Softplus negative binomial Integer-valued Generalized Autoregressive Conditional Heteroskedasticity (sp NB- INGARCH) model and establishing its stationarity properties, alongside methodology for parameter estimation. Building upon this foundation, the Neural negative binomial INGARCH (neu - NB-INGARCH) model is proposed, designed to enhance predictive accuracy while accommodating moderate non-stationarity in count time series data. A simulation study and data analysis demonstrate the efficacy of the sp NB-INGARCH model, while the practical utility of the neu - NB - INGARCH model is showcased through a comprehensive analysis of a healthcare data. Additionally, a thorough literature review is presented, focusing on the application of neural networks in time series modeling, with particular emphasis on count time series. In short, this work contributes to advancing the theoretical understanding and practical application of neural network-based models in count time series forecasting.