Determination of the best weight matrix for the Generalized Space Time Autoregressive (GSTAR) model in the Covid-19 case on Java Island, Indonesia

Abstract

One factor that goes into the construction of a space–time model, in this case, the Generalized Space–Time Autoregressive (GSTAR) model, is the weight matrix, which acts as a spatial representation and illustrates the relationship that exists between different locations. The temporal and spatial correlations are both accounted for in this model simultaneously. The accuracy with which the weight matrix is chosen significantly impacts the prediction results. The distance inverse and uniform weight matrices are two examples of weight matrices utilized frequently. A recent study on the adjustment of the weight matrix uses distance with rail transit, queen contiguity matrices, and techniques with graph theory. This research aims to find a weight matrix that closely resembles the real-world spatial context by analyzing and contrasting the five weight matrices presented earlier. Afterward, the weight matrix is fed into the GSTAR model as an input variable. In this article, each weight matrix’s various properties will be broken down and analyzed in detail. The case study used in preparation for the Christmas and New Year’s celebrations in 2023 focused on the daily increase in Covid-19 cases across six provinces on Java Island, Indonesia. The Java island was selected as Indonesia’s capital because it serves as the country’s economic hub and connects all provinces to one another. This enables large-scale spatial links between sites with the same time lag or different time delays. According to the findings that were uncovered, the MST weight matrix is the one that should be utilized, and it should have a prediction error tolerance of 19%.