Modeling Dependence Dynamics of Air Pollution: Pollution Risk Simulation and Prediction of PM$_{2.5}$ Levels

Abstract

The first part of this paper introduces a portfolio approach for quantifying the risk measures of pollution risk in the presence of dependence of PM$_{2.5}$ concentration of cities. The model is based on a copula dependence structure. For assessing model parameters, we analyze a limited data set of PM$_{2.5}$ levels of Beijing, Tianjin, Chengde, Hengshui, and Xingtai. This process reveals a better fit for the t-copula dependence structure with generalized hyperbolic marginal distributions for the PM$_{2.5}$ log-ratios of the cities. Furthermore, we show how to efficiently simulate risk measures clean-air-at-risk and conditional clean-air-at-risk using importance sampling and stratified importance sampling. Our numerical results show that clean-air-at-risk at 0.01 probability level reaches up to 352 {\mu}gm-3 (initial PM$_{2.5}$ concentrations of cities are assumed to be 100 {\mu}gm-3) for the constructed sample portfolio, and proposed methods are much more efficient than a naive simulation for computing the exceeding probabilities and conditional excesses. In the second part, we predict PM$_{2.5}$ levels of the next three-hour period of four Chinese cities, Beijing, Chengde, Xingtai, and Zhangjiakou. For this purpose, we use the pollution and weather data collected from the stations located in these four cities. Instead of coding the machine learning algorithms, we employ a state-of-the-art machine learning library, Torch7. This allows us to try out the state-of-the-art machine learning methods like long short-term memory (LSTM). Unfortunately, due to small data size and lots of missing values (when we combined the features of the cities) in the data, LSTM does not perform better than a multilayer perceptron. However, we get a classification accuracy above 0.72 on the test data.