Spatio-Temporal Time Series Forecasting Using an Iterative Kernel-Based Regression

Spatio-temporal time series analysis is a growing area of research that includes different types of tasks, such as forecasting, prediction, clustering, and visualization. In many domains, like epidemiology or economics, time series data are collected to describe the observed phenomenon in particular locations over a predefined time slot and predict future behavior. Regression methods provide a simple mechanism for evaluating empirical functions over scattered data points. In particular, kernel-based regressions are suitable for cases in which the relationship between the data points and the function is not linear. In this work, we propose a kernel-based iterative regression model, which fuses data from several spatial locations for improving the forecasting accuracy of a given time series. In more detail, the proposed method approximates and extends a function based on two or more spatial input modalities coded by a series of multiscale kernels, which are averaged as a convex combination. The proposed spatio-temporal regression resembles ideas that are present in deep learning architectures, such as passing information between scales. Nevertheless, the construction is easy to implement, and it is also suitable for modeling data sets of limited size. Experimental results demonstrate the proposed model for solar energy prediction, forecasting epidemiology infections, and future number of fire events. The method is compared with well-known regression techniques and highlights the benefits of the proposed model in terms of accuracy and flexibility. The reliable outcome of the proposed model and its nonparametric nature yield a robust tool to be integrated as a forecasting component in wide range of decision support systems that analyze time series data.