KONSTRUKSI MODEL GENERALIZED SPACE TIME AUTOREGRESSIVE WITH SEASONAL EXOGENOUS VARIABLE (GSTAR-SX)

• Main Author: Utami, Riani
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/81277
• Institution: Institut Teknologi Bandung

The current development of space-time models is progressing rapidly, one of which is the GSTAR (Generalized Space Time Autoregressive) model. The GSTAR model assumes that events at a certain location are influenced by events at that location and its neighboring locations at previous times. Over time, some researchers have added the assumption that events at a location are influenced not only by space and time but also by other variables, referred to as exogenous variables. Thus, the GSTAR-X model (Generalized Space Time Autoregressive with Exogenous Variables) was developed. However, the development of the GSTAR-X model so far has not considered the data patterns of exogenous variables, such as if the exogenous variable contains seasonal patterns. Therefore, in this study, a new model called GSTAR-SX (Generalized Space Time Autoregressive with Seasonal Exogenous Variable) is constructed. By introducing the seasonal factor in the exogenous variable, the GSTAR-SX model is expected to provide a more comprehensive and accurate understanding of data patterns and trends in a spatial-temporal context. Thus, constructing the GSTAR-SX model becomes essential to improve prediction accuracy and enhance the model's ability to anticipate significant seasonal variations in the data. The objectives of this study are to formulate the GSTAR-SX model equations, estimate the parameters of the GSTAR-SX model, and apply the GSTAR-SX model to the case of Dengue Fever in Semarang with suhu as the exogenous variable. Constructing the GSTAR-SX model equations is crucial because it considers the seasonal parameter of the exogenous variable, which often occurs in predictions using the GSTAR-X model. In this process, seasonal parameters are added to the regular GSTAR-X model equations, enabling the GSTAR-SX model to more accurately capture data patterns and trends influenced by seasonal factors. Parameter estimation of the GSTAR-SX model is carried out by considering the additional parameters that arise due to the inclusion of the seasonal variable. Thus, constructing the GSTAR-SX model provides a more holistic approach to spatial-temporal data analysis, relevant to improving prediction accuracy and enhancing the model's ability to anticipate significant seasonal variations in the data. In this study, the GSTAR-SX model is constructed by considering three different spatial weights: uniform weights, inverse distance weights, and normalized cross-correlation weights. The use of this model aims to understand and predict the spatial and temporal patterns of response data across various locations. Identification of the GSTAR-SX model is performed using STACF plots, STPACF plots, ACF plots, and CCF plots. Meanwhile, parameter estimation is conducted using the Least Squares (LS) method. Model accuracy results are assessed using RMSE (Root Mean Square Error) and MAPE (Mean Absolute Percentage Error) values. The case study for the GSTAR-SX model is applied to the Dengue Fever cases in 16 districts in Semarang City, namely Banyumanik, Candisari, Gajah Mungkur, Gayamsari, Genuk, Gunung Pati, Mijen, Ngalian, Pedurungan, West Semarang, South Semarang, Central Semarang, East Semarang, North Semarang, Tembalang, and Tugu. The case study analysis results indicate that the chosen GSTAR-SX model order is GSTAR-SX(1;1)(1;1)12. The GSTAR-SX(1;1)(1;1)12 model represents that Dengue Fever incidents at a location are influenced by Dengue Fever incidents at that location and its neighboring locations at one previous time, and influenced by suhu at that location and its neighboring locations at one previous time. The model accuracy results show variations in the GSTAR-SX model performance across different locations, with different MAPE results depending on the spatial weights used. Cross-correlation weights proved to be an important factor in improving prediction accuracy in several locations.