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Journal of Mathematics, Computation and Statistics (JMATHCOS)
Published by Universitas Negeri Makassar
ISSN : 24769487     EISSN : 27210863     DOI : https://doi.org/10.35580/jmathcos
Core Subject : Education,
Mathematics
Fokus yang didasarkan tidak hanya untuk penelitian dan juga teori-teori pengetahuan yang tidak menerbitkan plagiarism. Ruang lingkup jurnal ini adalah teori matematika, matematika terapan, program perhitungan, perhitungan matematika, statistik, dan statistik matematika.
Arjuna Subject : Matematika - Matematika Terapan
Articles 241 Documents
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Integrating Spatial Lag and Error Components in a SARMA Model for Tuberculosis Analysis across Indonesian Provinces Zakiyah Mar'ah; Rahmat H.S.
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/107vez06

Abstract

Tuberculosis (TB) remains a critical public health challenge, necessitating an in-depth understanding of its regional determinants to formulate effective, targeted interventions. This study investigates the underlying factors driving TB cases and identifies the optimal spatial regression model for analyzing its regional distribution. Utilizing cross-sectional data from 34 observation areas during the year 2023, the prevalence of TB was evaluated against five independent variables: life expectancy (X1), access to basic sanitation (X2), availability of primary healthcare facilities (X3), smoking prevalence (X4), and treatment success rates (X5). Initial exploratory analysis revealed a significant spatial autocorrelation of TB cases across the regions (Moran’s I = 0.566, p-value = 0.0003). Consequently, spatial regression modeling was applied using Spatial Autoregressive (SAR), Spatial Error Model (SEM), and Spatial Autoregressive Moving Average (SARMA) approaches. By comparing the Akaike Information Criterion (AIC), Log-Likelihood, and R² metrics, the SARMA model emerged as the most robust fit for the dataset (R² = 0.674, AIC =283.82). The empirical results demonstrate that, at a 10% significance level, access to basic sanitation negatively impacts TB cases. Furthermore, the significance of the spatial parameters confirms that neighboring regional dynamics and geographical proximity play a crucial role in the spread of Tuberculosis.
Application of the Light Gradient Boosting Machine (LightGBM) Method in Predicting the Risk of Anemia Rani Islamiyati; Siti Amiroch; Awawin Mustana Rohmah; Dicka Yale Kardono
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/p3aany94

Abstract

Anemia is one of the public health problems that requires serious attention, considering the relatively high percentage of anemia cases across various regions, including mild, moderate, and severe levels. To reduce the number of cases, a method capable of accurately predicting the risk of anemia is needed. This study aims to identify the most influential features in predicting the risk of anemia and to assess the performance of the LightGBM method in predicting this risk. The research process began with several stages: preprocessing, feature selection using the mutual information method, data balancing with SMOTE, parameter optimization via grid search, and evaluation of the LightGBM method on Complete Blood Count (CBC) data from hematology laboratory tests. The results indicate that the top 6 features out of the 16 in the original dataset are Hb, RBC, LYMP, HCT, MCV, and MCH. The application of the LightGBM method yielded optimal performance with an accuracy exceeding 97% and an AUC of 0.99. These values demonstrate that the LightGBM method possesses optimal capability in predicting the risk of anemia.
Implementation of Long Short-Term Memory for Forecasting the Indonesian Rupiah Exchange Rate against the Saudi Arabian Riyal Lisna Fauziyah; Siti Amiroch; Siti Alfiatur Rohmaniah
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/4b0ct819

Abstract

Exchange rates are a key indicator of a country’s economic condition and are inherently volatile and difficult to predict. Indonesian Rupiah exchange rate against Saudi Arabian Riyal (SAR) exhibits complex time series characteristics influenced by various macroeconomic factors. This study aims to forecast the Rupiah–SAR exchange rate using the Long Short-Term Memory (LSTM) method. The dataset consists of secondary data obtained from Bank Indonesia, covering the period from January 2, 2015, to February 27, 2026, with a total of 2,725 observations. The research methodology includes data preprocessing, transformation using a sliding window approach, data splitting, and LSTM modeling with hyperparameter tuning. The best performing model from the research results shows that achieved with a 90:10 train–test split, using 32 LSTM units, a learning rate of 0.001, 100 epochs, a dropout rate of 0.1, and a batch size of 32, yielding a Mean Absolute Percentage Error (MAPE) of 0.240376%, which falls into the highly accurate category. The 30-day forecasting results show a gradual downward trend in the exchange rate. These findings suggest that the LSTM model not only provides high predictive accuracy but also effectively captures the underlying nonlinear dynamics and temporal dependencies of exchange rate movements. Furthermore, the results reflect broader economic interactions, indicating that the model outputs can be utilized as a practical reference for financial planning and economic decision-making.
Multivariate Analysis of Regional Economic Resilience Capacity Using PCA, Gaussian Mixture Model, and Random Forest Dian Septiana; Fanny Ramadhani; Sisti Nadia Amalia; Fahmi Ashari S. Sihaloho
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/qbm5kx46

Abstract

Economic resilience capacity has become an important issue in regional development because socio-economic disparities influence the ability of regions to adapt to structural pressures and external disturbances. However, measuring regional resilience capacity remains challenging due to the multidimensional and interrelated nature of socio-economic indicators. This study analyses regional economic resilience capacity in North Sumatra using an integrated multivariate statistical and machine learning framework combining Principal Component Analysis (PCA), Gaussian Mixture Model (GMM), and Random Forest. PCA was employed to construct a composite Economic Resilience Capacity Index (ERCI) from socio-economic indicators, while GMM clustering was applied to identify regional typologies within the reduced dimensional space. The initial clustering estimation identified North Nias as an extreme singleton cluster, indicating the presence of an outlier observation. After excluding the outlier, the final GMM model selected a four-cluster spherical covariance structure based on the Bayesian Information Criterion (BIC). A comparison with K-means clustering produced different optimal grouping structures, indicating sensitivity to clustering assumptions and the complexity of regional socio-economic patterns. The first two principal components explained approximately 72% of the total variance, indicating adequate representation of the dominant socio-economic structure. The geographical distribution of clusters reveals substantial regional heterogeneity, where regions in the Nias area are concentrated within the low resilience capacity cluster, while urban and economically integrated regions form distinct growth-oriented clusters. Random Forest analysis indicates that unemployment and poverty related indicators are the most influential variables in distinguishing regional resilience typologies. Furthermore, the comparison between ERCI and GMM results shows that regions with relatively similar index values may still belong to different clusters, indicating that regional resilience patterns do not necessarily follow a single linear socio-economic structure. These findings suggest that regional economic resilience capacity in North Sumatra is shaped by multidimensional structural disparities rather than by a single composite index alone.
Comparison of Backpropagation Neural Network and Long Short-Term Memory for Rainfall Prediction in Lamongan Regency Andri Hardiyansyah; Siti Amiroch; Siti Alfiatur Rohmaniah
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/n2b8sn30

Abstract

Rainfall is one of the important factors in the agricultural sector and water resource management especially in Lamongan Regency, which has a seasonal rainfall pattern. Variability and uncertainty of rainfall can affect agricultural activities as well as water availability for irrigation needs and water resource management. As an effort to minimise crop failure, an accurate prediction method is needed to support future planning. This study aims to predict rainfall using Backpropagation Neural Network and Long Short-Term Memory (LSTM) methods, as well as to compare the performance of both methods to determine the most optimal method in rainfall prediction to support planting time planning and water management. The data used are historical rainfall data, particularly from areas known as rice production centres in Lamongan Regency. The data underwent preprocessing stages, including data cleaning, normalisation, and time series data formation. The models were trained using three data splitting scenarios, namely 70:30, 80:20, and 90:10, and were then evaluated using the Root Mean Square Error (RMSE). The best model was determined based on the smallest RMSE value and subsequently used to predict rainfall for the next year. The results show that the best model was obtained using the LSTM method, with RMSE values of 24.70 mm for Lamongan, 26.74 mm for Kembangbahu, 44.77 mm for Tikung, 33.12 mm for Sugio, and 33.67 mm for Sukodadi. Therefore, the LSTM method is considered more optimal than the Backpropagation method in predicting rainfall in Lamongan Regency. The effective rice planting period occurs from May to July, as rainfall during this period is relatively sufficient and stable to support crop growth. In addition, planting activities can be carried out two to three times in a year.
Forecasting Passenger Volume at Sultan Hasanuddin Airport in Makassar Using the Support Vector Regression Method Maya Sari Wahyuni; Irwan Irwan; Asria Asria
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/x5wqjd81

Abstract

The number of passengers at Sultan Hasanuddin Airport in Makassar fluctuates from year to year, requiring an accurate forecasting method to support planning and decision-making. This study discusses the application of the Support Vector Regression(SVR) method in forecasting the number of passengers at Sultan Hasanuddin Airport, Makassar City. SVR is a forecasting model used to predict nonlinear time series data. The data used is secondary data on the number of monthly domestic flight departures from January 2006 to December 2024 obtained from the Central Statistics Agency. The research stages included data normalization using the min-max method, the formation of supervisory data using a sliding window with a window size of 12, the division of data into training (80%) and Testing (20%), and modeling using SVR with a Radial Basis Function (RBF) kernel. The selection of optimal SVR parameters was carried out through Grid Search Optimization, with the best parameter results being epsilon (ε)=0, Cost(C)= , Gamma (γ)= . Evaluation using Mean Absolute Percentage Error (MAPE) resulted in a value of 16.43%, which is classified as good accuracy. Forecasting for the period January–December 2025 produced a pattern of passenger numbers fluctuating between 232.534 and 280.842.
SETL Mathematical Modeling of Early Marriage Dynamics in Wajo Regency Irwan Irwan; Sitti Aisyah; Maya Sari Wahyuni; Syafruddin Side
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/tf98kc30

Abstract

Early marriage is a social problem that has long-term impacts on the psychological well-being, education, and overall welfare of adolescents in Wajo Regency. This study constructs and analyzes an SETL (Susceptible, Entice, Tied, Liberated) mathematical model to describe the dynamics of early marriage in Wajo Regency. The model consists of a system of differential equations accompanied by equilibrium point analysis, local stability analysis, the basic reproduction number, and numerical simulations. Data were obtained through quantitative questionnaires administered to adolescent respondents. The results show two stable equilibrium points and values of  for SMP Negeri 2 Pammana and   for SMA Negeri 9 Wajo. The simulation results indicate that the proportion of adolescents tied to early marriage is higher in the senior high school. Although the  values for both the junior and senior high schools are below one, they still require intervention due to social and cultural factors that continue to increase adolescents’ vulnerability to early marriage, such as family pressure, limited understanding of the risks associated with early marriage, and restricted access to information and counseling services. These social dynamics surrounding adolescents may sustain or even trigger an increase in early marriage cases if not accompanied by consistent and targeted preventive efforts. This finding underscores the importance of preventive interventions beginning at the elementary education level, with active involvement from families, schools, and relevant institutions in Wajo Regency.
Development of a Hybrid Model of Diffie–Hellman and Hill Cipher Based on Fuzzy Sets for Strengthening Cryptographic Key Security Armayani Arsal; Muh. Fachrul Latief
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/62jpw347

Abstract

In this paper, key security has been examined, which is a fundamental factor in cryptographic systems because the quality of the key significantly affects the algorithm's resilience against cryptanalysis attacks. This research aims to develop a hybrid cryptography model of Diffie-Hellman and Hill Cipher based on fuzzy sets. This hybrid model is designed by combining the advantages of Diffie–Hellman in the secure key exchange process with Hill Cipher as a matrix-based encryption algorithm. Fuzzy sets are used as an adaptive mechanism in the key generation and strengthening process to enhance the randomness, complexity, and uncertainty of the key value. The research methods include literature study, hybrid scheme design, fuzzy rule formulation, and implementation of encryption and decryption processes. The result of this research is the formation of a hybrid cryptography model capable of generating keys that are more difficult to predict, thereby strengthening data protection against potential cryptanalysis attacks.
Hybrid ARX–GARCH–LSTM Approach for Volatility Estimation of Indonesia’s Oil and Gas Sector Stocks: A Case Study of PGAS Ferigo Taufani Tri Hakiki; Irhamah Irhamah; Heri Kuswanto
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/rrv0zb05

Abstract

This study develops a hybrid ARX–GARCH–LSTM approach to estimate the volatility of PGAS stock during the 2010–2025 period. Stock volatility exhibits characteristics such as heteroskedasticity, volatility clustering, and nonlinear patterns, requiring an approach capable of capturing volatility dynamics more accurately. The proposed approach integrates the ARX model to capture the influence of external factors, the GARCH model to model time-varying volatility, and Long Short-Term Memory (LSTM) to learn nonlinear patterns from the residual/errors of the GARCH model. The modeling process begins by transforming stock prices into log returns, followed by ARX estimation to purify returns from the influence of exogenous variables. The ARX residuals are then modeled using GARCH(1,1), and the residual/errors generated by the GARCH model are subsequently used as input for the LSTM model to construct the hybrid ARX–GARCH–LSTM model. The results show that the hybrid ARX–GARCH–LSTM model outperforms the GARCH and baseline LSTM models with an RMSE value of 0.004250, an MAE value of 0.003077, and an R² value of 0.827293. Compared to the GARCH model, the hybrid approach reduces RMSE by 42.43% and MAE by 48.53%, while increasing the R² value by 72.83%. These findings indicate that the integration of statistical models and deep learning methods can improve the accuracy of stock volatility estimation and potentially support investment decision-making and financial risk management.
Evaluation of Imputation Methods for Clustering Categorical Time Series on Financial Sector Stock Data Rita Rahmawati; I Made Sumertajaya; Asep Saefuddin; Kusman Sadik
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/t5pe8v78

Abstract

Missing values in financial time series data can affect the information structure of the data and impact the clustering results obtained. This research aims to evaluate the performance of several time series data imputation methods on the quality of categorical time series clustering on financial sector stock data on the Indonesia Stock Exchange. The imputation methods compared include linear interpolation, spline interpolation, and Kalman smoothing. The research data is in the form of daily closing prices of 92 financial sector stocks for the period 2 January 2023 to 31 October 2025. Numerical clustering was carried out using K-Means Time Series based on Dynamic Time Warping (DTW), while categorical clustering was carried out using K-Medoids with the Gower distance measure in two categorization schemes, namely five and seven categories. Evaluation of suitability between numerical and categorical clustering was carried out using the Rand Index (RI), Fowlkes–Mallows Index (FMI), and Jaccard Index. The research results show that the imputation method produces different clustering qualities. Linear interpolation provides the best and most consistent performance compared to other methods, especially in the seven-category scheme with an RI value of 0.6417, FMI of 0.4338, and Jaccard Index of 0.3256. These results show that linear interpolation is better able to maintain the information structure of the data in the categorical time series clustering process compared to spline interpolation or Kalman smoothing.

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