The generalized STAR modeling with minimum spanning tree approach of spatial weight matrix - Mukhaiyar, Utriweni; Mahdiyasa, Adilan Widyawan; Sari, Kurnia Novita; Noviana, Nur Tashya (Frontiers in Applied Mathematics and Statistics, 2024)
The weight matrix is one of the most important things in Generalized Space-Time Autoregressive (GSTAR) modeling. Commonly, the weight matrix is built based on the assumption or subjectivity of the researchers. This paper proposes a new approach to compose the weight matrix using the Minimum Spanning Tree (MST) approach. This approach reduces the level of subjectivity in constructing the weight matrix, since it is based on the observations. The spatial dependency among locations is evaluated through the centrality measures of MST. It is obtained that this approach could give a similar weight matrix with the commonly used, even better in some ways, especially in modelling the data with higher variability. For the study case in traffic problems, the number of vehicles entering the Purbaleunyi toll was modeled by GSTAR with several weight matrix perspectives. According to Space-Time ACF-PACF plots, GSTAR(1;1), GSTAR(1;2), GSTAR(2;1,1) models be the candidates of appropriate models. Based on the root mean square errors and mean absolute percentage errors, it is concluded that the GSTAR(2;1,1) with MST approach is the best model to forecast the number of vehicles entering the Purbaleunyi toll. This best model is followed by GSTAR(1;1) with MST approach of spatial weight matrix.