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We develop a new method that combines a decision tree with a wavelet transform to forecast time series data with spatial spillover effects. The method can not only improve prediction but also give good interpretability of the time series mechanism. As a feature exploration method, the wavelet transform represents information at different resolution levels, which may improve the performance of decision trees. The method is applied to simulated data, air pollution and COVID time series data sets. In the simulation, Haar, LA8, D4 and D6 wavelets are compared, with the Haar wavelet having the best performance. In the air pollution application, by using wavelet transform-based decision trees, the temporal effect of air quality index including autoregressive and seasonal effects can be described as well as the spatial correlation effect. To describe the spillover spatial effect in contiguous regions, a spatial weight is constructed to improve the modeling performance. The results show that air quality index has autoregressive, seasonal and spatial spillover effects. The wavelet transformed variables have a better forecasting performance and enhanced interpretability than the original variables. For the COVID time series of cumulative cases, spatial weighted variables are not selected which shows the lock-down policies are truly effective.

Spatio-temporal forecasting using wavelet transform-based decision trees with application to air quality and covid-19 forecasting