Neuromorphic Computing and AI-Enhanced Modeling of Time Series Counts for Real-Life Data Analysis

Time series of counts find extensive applications in various domains such as public health, finance, trade volumes, and environmental monitoring. Dealing with dispersion in these count-based time series is crucial for effective modeling and prediction. In this context, we propose a novel approach using a flexible first-order integer-valued non-stationary autoregressive (INAR(1)) process with innovation terms following a Conway-Maxwell Poisson distribution (COM-Poisson). This INAR(1) COM-Poisson process accommodates time-varying covariates and provides a versatile framework for modeling different forms of dispersion. We explore various methods for estimating the model’s unknown parameters, including likelihood, quasi-likelihood, and Bayesian approaches. Through simulation tests and the application of the INAR(1) COM-Poisson model to real-world data from India, we evaluate the performance of different estimation methodologies. Our results indicate that the Generalized Quasi-Likelihood (GQL) methodology yields less biased estimates compared to previous approaches. Additionally, we analyze the model’s autocorrelation structure while considering time-varying covariates. These findings have far-reaching implications for decision-making and policy development in fields like public health, finance, and environmental management, and offer valuable insights for modeling time series of counts in various domains.