Hybrid VARX-SVR and GSTARX-SVR for forecasting spatio-temporal data

Generalized Space-Time Autoregressive or GSTAR model is a special form of Vector Autoregressive or VAR model and commonly used for forecasting spatio-temporal data. The objective of this study is to propose hybrid spatio-temporal methods by applying Support Vector Regression or SVR as a nonlinear machine learning method in two representations model, i.e. as VAR or GSTAR with exogenous variables known as VARX or GSTARX, respectively. These two proposed hybrid methods are then known as VARX-SVR and GSTARX-SVR model. These models consist of two steps modelling, i.e. the first step is modelling of trend, seasonal, and calendar variation effects using time series regression, and the residual of this first step is modelled by VARX-SVR and GSTARX-SVR in the second step. Both simulation and real data about inflow and outflow currency in three location of Bank Indonesia at West Java region are used as case studies. The results of simulation study show that both the proposed VARX-SVR and GSTARX-SVR models yield more accurate forecast in testing dataset than VARX and GSTARX. Furthermore, the results of real data showed that VARX is the best model for forecasting outflow in three locations and inflow in two locations. Meanwhile, GSTARX-SVR is the best model for forecasting inflow at one location of Bank Indonesia at Wes Java region. In general, these results in accordance with the third M3 forecasting competition conclusion, i.e. the more complicated model do not necessary yield better forecast than the simpler one.