Seasonal Multivariat Time Series Forecasting On Tourism Data by Using Var-Gstar Model

Abstract

This research intends to study a new approach VAR-GSTAR (Vector Autoregressive-General Space-Time Autoregressive) model for forecasting seasonal multivariate time series. The parameters of the model are estimated by Least Squares method. In this research, we also derive the asymptotic properties of the parameter estimator, which yield the consistency and multivariate normal asymptotes distribution. Based on those properties, we build the procedure for finding the best model in seasonal multivariate time series, and then apply it on the number of foreign tourists in Yogyakarta and Bali data. The result from VAR-GSTAR model is compared with the result from the standard multivariate time series. The comparison result demonstrates that the procedure of VARMA model can not carry out the seasonal lags on the order of the model. This problem can be handled by the VAR-GSTAR model. The interpretation of VAR-GSTAR model is more realistic than that of VARMA model, i.e. the number of foreign tourists in Yogyakarta depends on that in Bali, but not the opposite, whereas VARMA model yields the opposite result. Additionally, the result of forecast accuracy comparison on tourism data in Yogyakarta and Bali shows that VAR-GSTAR model give better forecast than VARMA model.