A multivariate Birnbaum-Saunders autoregressive moving average model with application to air pollution concentration data

TL;DR

This paper introduces a multivariate Birnbaum-Saunders autoregressive moving average model with exogenous variables for analyzing correlated positive skewed environmental data, demonstrated on air pollution concentrations.

Contribution

It develops a novel multivariate BS ARMA model with EM-based estimation for joint analysis of asymmetric time series with exogenous factors.

Findings

Model performs well in simulation studies across various correlation levels.

Application to Chilean air pollution data shows the model's effectiveness.

Proposed methodology captures the dynamics of PM2.5 concentrations accurately.

Abstract

Fine particulate matter (PM$_{2.5}$) concentration data are positive, right-skewed series that arise naturally in environmental monitoring and are well described by the Birnbaum-Saunders (BS) distribution. In this paper, we propose a multivariate BS autoregressive moving average (MBSARMA) model with exogenous terms for the joint analysis of correlated positive asymmetric time series. The proposed model combines the multivariate log-linear BS framework with dynamic autoregressive moving average components on the conditional location parameter of each response. We estimate the model parameters by means of the Expectation-Maximisation (EM) algorithm. The performance of the proposed conditional likelihood estimators is evaluated by means of a Monte Carlo simulation study under several correlation levels and sample sizes. An application to weekly PM$_{2.5}$ pollution concentration data recorded at three monitoring stations in Santiago, Chile, obtained from the National Air Quality Information System of Chile (SINCA), is presented. The results show the good performance of the proposed methodology.