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CAUCHY: Jurnal Matematika Murni dan Aplikasi
Published by Universitas Islam Negeri Maulana Malik Ibrahim Malang
ISSN : 20860382     EISSN : 24773344     DOI : 10.18860
Core Subject : Education,
Mathematics
Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh Mitra Bestari (reviewer) untuk dinilai substansi kelayakan naskah. Redaksi berhak mengedit naskah sejauh tidak mengubah substansi inti, hal ini dimaksudkan untuk keseragaman format dan gaya penulisan.
Arjuna Subject : -
Articles 533 Documents
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Biclustering Performance of Iterative Signature Algorithm and Plaid Model after Imputation on Indonesian Macroeconomic Indicators Yani Prihantini Hiola; I Made Sumertajaya; Indahwati Indahwati
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.41933

Abstract

Biclustering is a two-way clustering method that identifies local patterns simultaneously across rows and columns of a data matrix. However, missing values may alter data structures and affect biclustering results. Studies evaluating the interaction between imputation methods and biclustering algorithms remain limited. This study evaluates the performance of the Iterative Signature Algorithm (ISA) and Plaid Model following imputation using Hot Deck, K-Nearest Neighbor (KNN), and Expectation Maximization (EM). The novelty of this study lies in assessing how the interaction between imputation methods and biclustering algorithms affects bicluster recovery and quality. Missing values were generated under MCAR at 5% and 10% proportions with 100 repetitions. Bicluster quality was evaluated using Mean Squared Residue (MSR), Transposed Virtual Error (VEt), and Sub-Matrix Correlation Score (SCS), while bicluster consistency was assessed using the Jaccard Index (JI). ISA consistently achieved higher JI values, indicating better preservation of bicluster structures, whereas the Plaid Model produced lower MSR, VEt, and SCS values, indicating more homogeneous biclusters. KNN generally showed the most consistent performance across scenarios. These findings suggest that imputation methods and biclustering algorithms should be selected jointly according to the analytical objective to obtain reliable biclustering results from incomplete macroeconomic data.
DeepSMOTE for Tea Leaf Disease Classification Using DenseNet-121 Transfer Learning Nikita Putri Insani; Sugiyarto Surono; Aris Thobirin
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.41693

Abstract

Data imbalance is a common problem in image classification that causes models to tend to be biased towards the majority class, so that the performance of the minority class decreases. To overcome this problem, this study applies the DeepSMOTE approach as a deep learning-based oversampling technique that produces synthetic images through interpolation in the latent space of the autoencoder. The balanced training data images were used to train the DenseNet-121 model through a transfer learning approach. Evaluations were carried out on three approaches, DeepSMOTE as the main approach, as well as two comparators, namely no augmentation and conventional augmentation. The results showed that DeepSMOTE had the highest accuracy, which was 97.73%, higher than the 8.99% non-augmentation approach and 4.49% from the conventional augmentation. F1-score value on minority classes such as Anthracnose increased by 0.2833 in the non-augmentation approach and 0.1318 in the conventional augmentation approach.These findings confirm that data balance plays an important role in improving model performance and that DeepSMOTE is able to provide a more even distribution of data thus supporting better generalization of image classification tasks.
Optimization of Imbalanced Class Using CTGAN and RSCV-Ensemble Learning for Clean Water Quality Classification Favian Sis Bagus Febrianto; Umu Sa'adah; Imam Nurhadi Purwanto
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.42071

Abstract

Class imbalance is a common challenge in classification learning. This condition often leads to poor model performance in identifying minority class observations. This study aims to evaluate the performance of an Ensemble Learning model optimized using Randomized Search CV (RSCV) to classify clean water quality under imbalanced class distributions. To address the imbalance problem, the CTGAN technique is applied and compared with other oversampling methods like SMOTENC that also can handle mix data. The model performance is assessed using two sided independent t-test form different mean (accuracy, precision, recall, F1-score, and AUC-ROC) two models. The best model performance from Data Testing in this study is the Ensemble Learning model with RSCV combined with CTGAN oversampling followed by mean Accuracy of 92,8%, mean Precision of 90,23%, mean Recall of 90,98%, mean f1-score of 90,82%, and mean AUC-ROC 96,80% from 25 split data experiment. Almost all accuracy metrics showed statistically significant differences when tested using a two-sided independent t-test. Overall, the results indicate that CTGAN outperforms SMOTENC, and RSCV optimization improves performance compared to models without optimization. Not only accuracy, all different mean Recall metrics is significant, further supporting the superiority of CTGAN and RSCV-enhanced models.
Adaptive Portfolio Rebalancing for NASDAQ-100 Stocks with Hippopotamus Optimization Algorithm under Transaction Costs Safrizal Ardana Ardiyansa; Mohamad Muslikh; Syaiful Anam
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.43876

Abstract

This study proposes a transaction cost-aware portfolio optimization framework for NASDAQ-100 stocks based on the Hippopotamus Optimization Algorithm (HOA). The mathematical model extends the classical mean-variance framework by incorporating transaction costs into a Net Sharpe Ratio (NSR) objective function. Daily adjusted closing prices of NASDAQ-100 constituent stocks from 2021 to 2025 are employed, with the twenty highest-ranked stocks according to the Sharpe Ratio (SR) selected as the candidate investment universe. Each optimization experiment is independently repeated 25 times to evaluate robustness and solution stability. The results indicate that the proposed HOA consistently achieves competitive optimization performance with very small variability across repeated runs throughout the investment horizon. Although several competing algorithms attain comparable or slightly better objective values during particular rebalancing periods, HOA remains among the strongest-performing methods while exhibiting stable convergence behavior. Throughout the investment horizon, the proposed algorithm produces the highest average cumulative portfolio value of \$5,307.87 \$125.71 from an initial investment of \$1,000, corresponding to an average annual return of 40.03% 0.68%, together with the highest average SR and NSR of 1.5736 0.0151, while maintaining competitive maximum drawdown and transaction costs. These findings demonstrate that incorporating transaction costs directly into the optimization objective enables HOA to achieve a favorable balance between portfolio growth, risk-adjusted performance, and trading efficiency under dynamic market conditions.
Bayesian Framework for Error Correction Model-Nonlinear Autoregressive Distributed Lag Meidy Indhira Putri; Nurjannah Nurjannah; Achmad Efendi; Ani Budi Astuti
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.42809

Abstract

This study proposes a Bayesian framework for estimating the Error Correction Model–Nonlinear Autoregressive Distributed Lag (ECM–NARDL) to analyze the dynamic and asymmetric relationship between inflation and economic growth in Indonesia. The model is estimated using Gibbs Sampling within a Markov Chain Monte Carlo (MCMC) framework, allowing parameter uncertainty to be evaluated through posterior distributions. Annual data from 1990–2024 are used for empirical analysis. Unit root tests indicate that the variables are integrated of order one, while the Bounds test confirms the existence of a long-run equilibrium relationship. The estimation results reveal a significant error-correction mechanism, suggesting that deviations from long-run equilibrium are corrected relatively quickly. The findings also indicate asymmetric effects of inflation, where decreases in inflation support long-run economic growth, while short-run increases in inflation negatively affect growth. Bayesian diagnostics and posterior predictive checks confirm the stability and adequacy of the proposed Bayesian ECM–NARDL framework.
Macroeconomic Determinants of Investment Credit in Indonesia: Evidence from the ARDL Bounds Testing Approach Nur Atikah; Nadia Kholifia; Lucky Tri Oktoviana; Muhammad Ilham Arif; Muhammad Nizar Hidayatullah; Vagustin Faharani; Mareta Putri Manunggal
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.42713

Abstract

Investment credit plays an important role in financing productive activities and sustaining Indonesia's economic development. Nevertheless, limited empirical evidence is available regarding how fluctuations in gold prices together with other macroeconomic indicators influence investment credit during the post-pandemic period. This study investigates the effects of gold prices, the USD/IDR exchange rate, the Industrial Production Index (IPI), the BI 7-Day Reverse Repo Rate, and inflation on investment credit using monthly observations from June 2016 to December 2024. An Autoregressive Distributed Lag (ARDL) model combined with an Error Correction Model (ECM) is employed to evaluate both long-run associations and short-run adjustments. The empirical findings reveal that the variables are cointegrated, implying the existence of a stable long-term equilibrium. However, none of the estimated long-run coefficients is statistically distinguishable from zero at conventional significance levels. In the short run, exchange rate movements generate the largest response in investment credit, whereas industrial production and the policy interest rate produce relatively modest effects. The error-correction coefficient is negative and statistically significant, indicating that temporary departures from equilibrium are gradually eliminated over time. These findings suggest that investment credit in Indonesia is driven primarily by short-term macroeconomic adjustments rather than persistent long-run effects of individual macroeconomic variables.
Danantara Effects on IDXESGL Stock Investment Strategies Using Single Index Model and VaR-Adjusted Sharpe Ratio Risky Gunawan; Evy Sulistianingsih; Shantika Martha; Yundari Yundari; Fida Fathiyah Addini
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.41334

Abstract

Danantara, established as Indonesia’s sovereign wealth fund on February 24, 2025, has introduced new dynamics in the Indonesian capital market. This study examines differences in portfolio strategies among IDX ESG Leaders (IDXESGL) index between the pre- and post-Danantara periods by comparing stock composition with positive expected returns and portfolio performance across two periods using the Single Index Model (SIM) and the Value at Risk-Adjusted Sharpe Ratio (VaRSR). The analysis employs an integrated framework that combines SIM for identifying best-performing stocks, a portfolio combination approach, and performance evaluation using the Sharpe ratio and VaRSR. This study utilized daily closing price data covering August 23, 2024, to February 23, 2025, as the pre-Danantara period, and February 24, 2025, to August 24, 2025, as the post-Danantara period. The results indicate that prior to Danantara’s establishment, optimal portfolios were dominated by digital-sector stocks, with higher performance than in the post-Danantara period. In contrast, the post-Danantara period is associated with greater exposure to conglomerates and state-owned enterprises with stronger fundamentals and lower downside risk. Overall, the findings suggest that the VaRSR yields a more conservative performance assessment and highlights a potential reorientation in investment strategies toward stability and resilience following Danantara’s establishment.
Hybrid ARIMAX–LSTM Modeling with Elastic Net for Time Series Forecasting the Education Index of Jambi Province Mhd. Teguh Arrozik; Tri Candra Nur Muhaimin; Melkisedek Sampari Koibur
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.40192

Abstract

Abstract This study proposes a Hybrid ARIMAX–LSTM framework integrated with Elastic Net regularization to improve the forecasting accuracy of the Education Index of Jambi Province. Annual data from 2010 to 2024 are utilized, with Elastic Net applied to select relevant exogenous variables and mitigate multicollinearity. The modelling strategy combines an ARIMAX (1,0,0) model to capture linear dynamics and the influence of selected explanatory variables, with a Long Short-Term Memory (LSTM) network to learn nonlinear patterns from ARIMAX residuals. The dataset is divided into training and testing subsets, where the model is trained using historical data and subsequently validated on unseen observations to assess its generalization capability. Forecasting performance is evaluated using Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE) on out-of-sample data for 2023 2024. Empirical results show that the proposed hybrid model with Elastic Net significantly outperforms the hybrid model without regularization, achieving an RMSE of 0.3677, an MAE of 0.2647, and a MAPE of 0.40%. In contrast, the ARIMAX–LSTM model with Elastic Net demonstrates substantially better predictive performance, with an RMSE of 0.0720, an MAE of 0.0714, and a MAPE of 0.11%. These findings demonstrate that Elastic Net enhances model generalization and improves residual learning in the LSTM component. After model evaluation, the hybrid models are further employed to generate forecasts of the Education Index for the period 2025–2027 to support medium-term educational planning. Overall, the proposed framework provides a robust and interpretable approach for forecasting regional educational indicators.
Dynamic Analysis of a Modified SETPR Terrorism Model Incorporating Recidivism of Imprisoned Terrorists Achla Fauziyah; Zulaikha Zulaikha
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.42029

Abstract

Terrorism poses a serious threat to national security, particularly when former terrorist inmates return to active duty due to the failure of deradicalization programs. This study modifies the $SETPR$ model by adding a direct recidivism path from the imprisoned compartment (\(P\)) to the active terrorist compartment (\(T\)) via the parameter \(k\). This model consists of five subpopulations: the susceptible (\(S\)), the exposed (\(E\)), active terrorists (\(T\)), imprisoned (\(P\)), and subpopulation that has ceased terrorist activities (\(R\)). The basic reproduction number is given by \(\mathcal{R}_0,\) which is derived using the next-generation matrix method and serves as a threshold parameter for the spread of terrorism. Local stability analysis shows that the terrorism-free equilibrium is locally asymptotically stable if \(\mathcal{R}_0 1\), while the endemic equilibrium is locally asymptotically stable if \(\mathcal{R}_0 1\). Numerical simulations using Matlab R2013a and Maple 11 show that when \(\mathcal{R}_0 = 0.0039 1\), the system converges to the terrorism-free equilibrium, meaning terrorism will become extinct. Conversely, with \(\mathcal{R}_0 = 5.8535 1\), the system is stable at the endemic equilibrium, indicating that terrorism persists at a positive level. These results show that it is important to control key parameters through integrated intervention strategies, so that the \(\mathcal{R}_0\) value can be reduced below unity.
Negative Binomial tv-DINGARCH Models for Monthly DHF Cases in Surabaya, Indonesia (2015-2025) Aminatuz Zahro; A'yunin Sofro
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.42667

Abstract

Count time series data are commonly encountered in epidemiological studies, such as monthly reports of Dengue Hemorrhagic Fever (DHF) cases. The INGARCH model has been widely used to handle temporal dependence and overdispersion in such data. However, the standard INGARCH model assumes constant dispersion, whereas in practice the dispersion level may vary over time due to epidemiological factors like seasonality or vector control policies. Accurately capturing this time-varying variability is essential for reliable disease surveillance. This study applies the tv-DINGARCH model to DHF cases in Surabaya from January 2015 to December 2025. The tv-DINGARCH(1,1,1,1) model with Negative Binomial distribution is used because it allows the dispersion parameter \(\phi_t\) to evolve dynamically. Parameter estimation is conducted using the Conditional Maximum Likelihood Estimation method implemented in RStudio. The results show that the tv-DINGARCH model yields AIC = 968.43 and BIC = 985.68, both smaller than those of the standard INGARCH model (AIC = 1012.18, BIC = 1023.68). The likelihood ratio test produces an LR statistic of 47.7560 with a p-value less than 0.000001, strongly rejecting constant dispersion. The stationarity condition is satisfied with \(\beta_2 + \alpha_2 + \beta_1 + \alpha_1 = 0.9990 1\). From a public health perspective, these findings indicate that the tv-DINGARCH model better captures the fluctuating dynamics of DHF transmission, supporting more effective surveillance and early warning systems.

Page 53 of 54 | Total Record : 533

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