Hybrid of Time Series Regression, Multivariate Generalized Space-Time Autoregressive, and Machine Learning for Forecasting Air Pollution

Abstract

The purpose of this study is to propose a new hybrid of space-time models by combining the time series regression (TSR), multivariate generalized space-time autoregressive (MGSTAR), and machine learning (ML) to forecast air pollution data in the city of Surabaya. The TSR model is used to capture linear patterns of data, especially trends and double seasonal. The MGSTAR model is employed to capture the relationship between locations, and the ML model is used to capture nonlinear patterns from the data. There are three ML models used in this study, namely feed-forward neural network (FFNN), deep learning neural network (DLNN), and long short-term memory (LSTM). So that there are three hybrid models used in this study, namely TSR-MGSTAR-FFNN, TSR-MGSTAR-DLNN, and TSR-MGSTAR-LSTM. The hybrid models will be used to forecast air pollution data consisting of CO, PM10, and NO2 at three locations in Surabaya simultaneously. Then, the performance of these three-combined hybrid models will be compared with the individual model of TSR and MGSTAR, two-combined hybrid models of MGSTAR-FFNN, MGSTAR-DLNN, MGSTAR-LSTM, and hybrid TSR-MGSTAR models based on the RMSE and sMAPE values in the out-of-sample data. Based on the smallest RMSE and sMAPE values, the analysis results show that the best model for forecasting CO is MGSTAR, forecasting PM10 is hybrid TSR-MGSTAR, and forecasting NO2 is hybrid TSR-MGSTAR-FFNN. In general, the hybrid model has better accuracy than the individual models. This result is in line with the results of the M3 and M4 forecasting competition.