Bayesian Modeling of Multivariate Integer-valued Autoregressive Processes

• Grant number: 25/06681-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: June 01, 2025
• End date: May 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Hedibert Freitas Lopes
• Grantee: Ricardo Cunha Pedroso
• Host Institution: Instituto de Ensino e Pesquisa (Insper). São Paulo , SP, Brazil
• Associated research grant: 23/02538-0 - Time series, wavelets, high dimensional data and applications, AP.TEM
• Associated scholarship(s): 26/16539-6 - A Bayesian Copula-based Modeling of Multivariate Integer-valued Autoregressive Processes, BE.EP.PD

Abstract

Integer autoregressive processes (INAR) play a vital role in the modeling of count series. In this project, we integrate a random environment that follows a state-space evolution into McKenzie's (1985) univariate INAR(1) model, and call our model Dynamic Multivariate INAR(1). The random environment provides an efficient and scalable multivariate generalization of the univariate INAR(1) model with dynamic multivariate negative binomial predictive distributions. Moreover, it also allows the Dynamic Multivariate INAR(1) model to consider time-varying contemporaneous dependence structures. We propose a Markov Chain Monte Carlo method and a Particle Learning Filter for parameter learning and for inference of state variables. In experiments based on real data sets, we will show that the Dynamic Multivariate INAR(1) model tends to substantially outperform competing models in terms of out-of-sample predictions one step ahead. (AU)