Application of Inverse of Autocovariance Matrix Method on Multivariate GSTAR (MGSTAR) Model For Predicting Economic Variable Data in Java Island Widhiya Nurqisthina Fadhila, Utriweni Mukhaiyar, Sandy Vantika, Gantina Rachmaputri
Institut Teknologi Bandung
Abstract
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 farmers purchase prices, thereby worsening the welfare of the community with farmers livelihoods. This problem motivates to conduct research and forecasts related to inflation and farmers exchange rates so that the government can take appropriate actions to minimize possible economic risks. Inflation and farmers 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 areas, 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. The process is stationary if all the eigenvalues of the autoregressive parameter matrix are inside the unit circle. However, as the time order of the model increases, the characteristic equation will become more complicated, so it will be challenging to find the eigenvalues. In 2012, Mukhaiyar 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 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 farmers exchange rates (FER). Parameter estimation using distance inverse weighting in model building is obtained using the OLS method for MGSTAR. After getting 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 have the best autoregressive order in conducting data modelling. 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 for 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 1.46.
Keywords: Inverse of Autocovariance Matrix (IAcM), Multivariate GSTAR (MGSTAR), inflation, farmers exchange rate, West Java, Central Java, East Java
