APPLICATION OF INVERSE OF AUTOCOVARIANCE MATRIX METHOD FOR MULTIVARIATE GSTAR (MGSTAR) MODEL TO FORECAST ECONOMIC VARIABLES DATA IN JAVA ISLAND

• Main Author: Nurqisthina Fadhila, Widhiya
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/70811
• Institution: Institut Teknologi Bandung

At the end of 2022, the impact of inflation will be increasingly felt. Prices of essential commodities have increased over time, and some countries have even experienced economic difficulties due to inflation. Sooner or later, inflation will affect the farmer’s purchase prices, thereby worsening the welfare of the community with farmer’s livelihoods. This problem motivates to conduct research and forecasts related to inflation and farmer’s exchange rates so that the government can take appropriate actions to minimize economic risks that may occur. Inflation and farmer’s exchange rates are monthly time series data which are suspected to be influenced by location, so a space-time model is needed to carry out the analysis. The models commonly used to perform space-time analysis are the STAR and GSTAR models. However, these models can only be used to analyze time series data with one variable at several locations. In this research, the development of the GSTAR model will be used, which can combine many variables in many locations, namely the Multivariate GSTAR (MGSTAR) model. In making predictions, the space-time model must comply with the assumption of stationarity. The stationarity of space-time processes uses the principle that a process has a constant mean and variance throughout the observation time. Just like the GSTAR model, the MGSTAR model can also be defined as stationary by utilizing the VAR form of the model. If all the eigenvalues of the autoregressive parameter matrix are inside the unit circle, then the process is stationary. However, as the time order of the model increases, the characteristic equation will become more complicated so that it will be difficult to find the eigenvalues. Mukhaiyar (2012) developed a new alternative method for examining the stationarity of the GSTAR model, namely the inverse approach of the autocovariance matrix or IAcM. Adapting from this research, in this study, we will look for IAcM to check the stationarity of the MGSTAR model. The results show that the IAcM method for MGSTAR is similar to the IAcM method for GSTAR. The only difference between the two method is that the IAcM for the MGSTAR model expands as the number of variables increases. The MGSTAR modelling procedure will be applied to forecast monthly economic data in several provinces in Java, namely West Java, Central Java and East Java with economic variables consisting of inflation and farmer’s exchange rates (FER). By using distance inverse weighting, parameter estimation in model building is obtained using the OLS method for MGSTAR. After obtaining a suitable model for inflation and FER data, a diagnostic test will be carried out on the model. In this study, the stationarity diagnostic test of the model will be carried out through an alternative approach, namely using IAcM on the MGSTAR model. The results of the stationarity check through IAcM will be compared with the stationary check through the eigenvalue approach. The AIC value indicates that the MGSTAR(1;1) and MGSTAR(2;1,1) models are the models with the best autoregressive order in conducting data modeling. Examination through the IAcM approach yields different conclusions from the eigenvalue approach which says that the two models are stationary. Even so, the forecast results of the MGSTAR(1;1) and MGSTAR(2;1,1) models are pretty good, and this is indicated by the small RMSE values of the two models, namely 1.38 and 1.53.