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All Journal International Journal of Quantitative Research and Modeling Jurnal Matematika Integratif
Audina, Yurid
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Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Electrical & Electronics Engineering Engineering Environmental Science Mechanical Engineering Physics Transportation

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Application of the Leslie Matrix on Female Birth Rates and Life Expectancy in the Special Region of Yogyakarta Lianingsih, Nestia; Haq, Fadiah Hasna Nadiatul; Audina, Yurid
International Journal of Quantitative Research and Modeling Vol 5, No 3 (2024)
Publisher : Research Collaboration Community (RCC)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijqrm.v5i3.761

Abstract

This study aims to predict the number and growth rate of the female population in the Special Region of Yogyakarta for 2025, using the Leslie Matrix model. The matrix utilizes fertility rates and female life expectancy across different age intervals. The data used includes the female population from 2015 and 2020, alongside Age-Specific Fertility Rate (ASFR) data for the same period. By applying the dominant eigenvalue of the Leslie matrix, the study finds that the growth rate of the female population in Yogyakarta is projected to increase, with a dominant eigenvalue of 1.252. The female population is predicted to reach 2,409,852 by 2025, an increase from 1,983,800 in 2020. These findings are expected to inform population management and development planning in Yogyakarta.
Application of Spatial Weight Matrix based on Semivariogram in Space-Time Autoregressive Integrative (STARI) Model for Financial System Forecasting in the Greater Bandung Region audina, yurid; Ruchjana, Budi Nurani; Abdullah, Atje Setiawan
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.69207.101-118

Abstract

The global financial crisis of 2022 had a significant impact on the stability of Indonesia’s financial sector, marked by fiscal expansion and an increase in the money supply. The uneven distribution of liquidity across regions generated disparities in regional inflation, resulting in macroeconomic dynamics that exhibited a complex spatio-temporal structure. These conditions require a forecasting approach capable of capturing spatial and temporal interactions simultaneously. This study applies the Space Time Autoregressive Integrated (STARI) model to describe monthly inflation dynamics that are non-stationary due to inter-regional trends within Bandung Raya area. Spatial dependence is represented through spatial weight matrices constructed using three approaches matrices: uniform weights, inverse-distance weights, and isotropic semivariogram weights derived from population density data. Their effects on forecasting accuracy are compared using the Mean Squared Error (MSE). The novelty of the proposed approach lies in the use of an isotropic semivariogram as the basis for constructing spatial weights, allowing the model to capture continuous and heterogeneous spatial autocorrelation beyond traditional distance-based methods. Model parameters are estimated using Ordinary Least Squares (OLS) method implemented through Python scripts, and model evaluation is conducted using forecasting accuracy criteria and error diagnostics. The results indicate that the STARI(1,1,1) model incorporating semivariogram-based spatial weights outperforms both uniform and inverse-distance weights in terms of forecasting accuracy, because it has a minimum MSE. These findings provide valuable insights for economic policy formulation in Bandung Raya area.
Co-Authors Atje Setiawan Abdullah Budi Nurani Ruchjana Haq, Fadiah Hasna Nadiatul Lianingsih, Nestia