07: Modeling Multivariate Positive Valued Time Series: An Application to Air Pollution Data

Music City Center 

Multivariate positive-valued time series are ubiquitous in many application domains including environment, finance, insurance, etc. We describe a Bayesian approach for dynamic modeling and forecasting of multivariate positive- valued time series with multivariate gamma distributions. We discuss a flexible level correlated model (LCM) framework which allows us to combine marginal gamma distributions for the positive‐valued component responses, while accounting for association among the components at a latent level. We introduce vector autoregressive evolution of the latent states, deriving its precision matrix and implementing fast approximate posterior estimation using integrated nested Laplace approximation (INLA). We use the R‐INLA package, building custom functions to handle our framework. We use the proposed approach to jointly model hourly concentrations of the air pollutants PM 2.5 and Ozone as a function of other pollutants, and weather variables. Our goal is to do a comparative temporal analysis of the air pollution in New Delhi with other polluted cities such as Los Angeles. In New Delhi, we analyze data from each of 22 air pollution monitoring stations from January 2018 to August 2023. Together with the analysis of the aggregate pollution in the city over time will help us understand different useful patterns in the pollution in New Delhi and its surrounding regions. This is joint work with Nalini Ravishanker (University of Connecticut), Anirban Chakraborti (Jawaharlal Nehru University) and Sourish Das (Chennai Mathematical Institute).