Hybrid Space-Time Model and Machine Learning for Forecasting Multivariate Spatio-Temporal Data

The purpose of this study is to propose a hybrid model by combining statistical methods, namely Time Series Regression (TSR), Multivariate Generalized Space-Time Autoregressive (MGSTAR) as a space-time model, and Machine Learning (ML) to forecast multivariate Spatio-temporal data simultaneously. The linear model, namely TSR is used to capture trends and double seasonal patterns. MGSTAR is a model for capturing dependencies between locations. Meanwhile, capturing nonlinear patterns used the ML model. In this study, three types of ML model is used, i.e., Deep Learning Neural Network (DLNN), Feed Forward Neural Network (FFNN), and Long Short-Term Memory (LSTM). We apply this proposed method to simulated data. Based on the Root Mean Square Error (RMSE) value, the proposed hybrid methods, namely TSR-MGSTAR-DLNN, TSR-MGSTAR-FFNN, and TSR-MGSTAR-LSTM, outperform other models such as TSR, MGSTAR, MGSTAR.-DLNN, MGSTAR-FFNN, MGSTAR-LSTM, and TSR-MGSTAR, especially when the data contain nonlinear noise components. The results also show that the proposed hybrid model can tackle complex patterns on Spatio-temporal data containing trends, double seasonal, linear noise, nonlinear noise, and dependencies between locations.