MODIFIED WEIGHT MATRIX USING PRIM’S ALGORITHM IN MINIMUM SPANNING TREE (MST) APROACH FOR GSTAR(1;1) MODEL

  • Nur'ainul Miftahul Huda Mathematics Department, Universitas Tanjungpura, Indonesia
  • Fransiskus Fran Mathematics Department, Universitas Tanjungpura, Indonesia
  • Yundari Yundari Mathematics Department, Universitas Tanjungpura, Indonesia
  • Lisa Fikadila Mathematics Department, Universitas Tanjungpura, Indonesia
  • Fauziah Safitri Mathematics Department, Universitas Tanjungpura, Indonesia
DOI: https://doi.org/10.30598/barekengvol17iss1pp0263-0274
Keywords: Spatial, Prim, Modified weight

Abstract

The Generalized Space-Time Autoregressive (GSTAR) model is able to utilize modeling of both space and time simultaneously. The existence of a weight matrix is one of the aspects that established this model. The matrix illustrates the spatial impact that occurs between locations. In this research, a modified weight matrix is presented using the Minimum Spanning Tree approach of graph theory. Prim's algorithm is utilized for calculation here. Not only does the modified weight matrix depend distance, but also highlights the correlation. It makes the modified weight matrix unique. Before starting Prim's algorithm, the correlation is first utilized as an input in forming the initial graph. Following that, find the graph with the least of MST weight. Afterwards, the graph is described utilizing weight matrix, which is applied to the normalization process. Following this, the GSTAR(1;1) modelling process is carried out, beginning with estimating the parameters and then forecasting. The case study is Covid-19 cases that occurred on Java Island between July 2020 (when early Covid-19 entered Indonesia) and the beginning of January 2021. The aim of the research is to model the Covid-19 cases using modified weights and to predict the following five times. The outcome is a GSTAR(1;1) model with modified weights can captures both temporal and spatial patterns. The accuracy of the model is achieved for both the training data and the testing data by the MAPE computations, which yielded of 11.40% and 21.57%, respectively. Predictions are also obtained for each province in the next five times.

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Published
2023-04-16
How to Cite
[1]
N. Huda, F. Fran, Y. Yundari, L. Fikadila, and F. Safitri, “MODIFIED WEIGHT MATRIX USING PRIM’S ALGORITHM IN MINIMUM SPANNING TREE (MST) APROACH FOR GSTAR(1;1) MODEL”, BAREKENG: J. Math. & App., vol. 17, no. 1, pp. 0263-0274, Apr. 2023.
Issue
Vol 17 No 1 (2023): BAREKENG: Journal of Mathematics and Its Applications
Section
Articles

Copyright (c) 2023 Nur'ainul Miftahul Huda, Fransiskus Fran, Yundari Yundari, Lisa Fikadila, Fauziah Safitri

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