Matrix-Variate Dynamic Linear Modelling with Forecasting of Multivariate Time Series Data With Application to Air Pollution in Athens

Abstract

Oxygen is one of the essential physiological needs for human and organisms to survive. Due to the increased burning of fossil fuels due to modernisation, industrialisation and other factors, the level of pollution in the air has increased. Human health is affected by many different types of diseases related to air pollution. In many countries, air pollution is a major concern, and a key reason for the reduction in the quality of life, as it increases the chance of certain lung diseases. Early forecasting of pollution levels might protect and enhance quality of life. Forecasting of air pollution levels is widely applied in many countries using different statistical tools. Matrix-variate dynamic linear models (MV-DLMs) are used in this project to predict the pollution levels of the air in Athens city by combining data from several different monitoring networks and meteorological information covariates. The MV-DLMs have been practised in applications where the interest lies in performing predictions or analysis of covariance structures through time series. The features of this model allow it to take into account the spatiotemporal structures and time varying regression presented in the data. Also, MV-DLMs can be applied on highly dimensional data, and with no restrictions in parameter space nor any need for simulations approaches. Exploratory data analysis has identified the need for data transformation and aggregation to be applied before modelling could be undertaken on air pollution observations. A simple log-transformation and weekly averaged aggregation were used to achieve improvements for applying the model. This paper is an application of the Bayesian procedure of multivariate gamma distributions for time series data, and the analysis involves matrix and time-varying state-space modelling, inference and forecasting. For this project, we aim to forecast air pollution levels using the data and the model presented in Bersimis and Triantafyllopoulos (2018). The forecasting results is for one week ahead, and it indicates a reasonable good fit for Athens air pollution data based on visual and error diagnostics of the fitting. The result of this study is useful for identifying areas with high air pollution and alerting the public in earlier sufficient time.