Development of generalized space time autoregressive integrated with ARCH error (GSTARI – ARCH) model based on consumer price index phenomenon at several cities in North Sumatera province

Inflation is defined as a situation where generally the price of goods has increased continuously. In order to measure inflation, Statistics of Indonesia (BPS) use the Consumer Price Index (CPI). Inflation in North Sumatera Province monitored through CPI change in several major cities which are Medan, Pematang Siantar, Sibolga, and Padangsidimpuan. The CPI value in these cities was affected by the previous times value and have correlation between one another. In data modeling, data that have correlation in time and spatial is called space time data. One of data modeling methods that can be used to analyze the space time data is the Generalized Space Time Autoregressive (GSTAR) which was introduced by Ruchjana (2002) with assumed constant variance error. Furthermore, time series data such as inflation often have high volatility which implicates on an inconstant value of variance and error. Nainggolan (2011) was introduced GSTAR model with an Autoregressive Conditional Heteroscedastic (ARCH) error, called GSTAR-ARCH model. In this model, the mean equation was modeled by GSTAR model and the variance equation was modeled by the ARCH model. For non stationarity data, we apply GSTAR-Integrated with ARCH error (GSTARI-ARCH) model, and the estimation parameters are using Generalized Least Square (GLS) method as introduced by Nainggolan (2011).