Multivariate air quality time series analysis via a recurrent variational deep learning model

Monitoring of air pollutants across space and time is critical in understanding pollution trends and reporting air quality. The Air Quality Index (AQI) is a tool used to communicate air quality that incorporates atmospheric concentrations of five major pollution indicators: ground-level ozone, particulate matter, carbon monoxide, sulfur dioxide, and nitrogen dioxide. The ability to accurately forecast these concentrations and identify unusual levels is of particular importance. In this work, we develop a generative time series model for air quality indicators and use it for long and short-term probabilistic forecasts. Air quality data are multivariate and exhibit high variability across indicators in both space and time. Marginal indicator distributions are typically skewed and contain substantial zeros, while indicator-wise cross-correlations can be highly non-linear. We find that hourly measurements additionally exhibit substantial temporal cross-correlation, long-term dependence, and daily periodicity. To capture these complexities, we employ a recurrent extension of the variational autoencoder (VAE) to sequential data. The VAE is a generative neural network architecture capable of learning complex, high dimensional manifolds on which data are distributed. Furthermore, recurrent architectures can capture non-linear and long-term temporal qualities of time series data. We train the proposed time series model on historical air quality measurements at multiple locations and demonstrate its ability to capture observed indicator-wise and temporal complexities. We additionally use the trained model to compute probabilistic forecasts and credible intervals of air quality indicators.