JURNAL GAUSSIAN (e-ISSN: 2339-2541) is an open access journal (e-journal) published since October 2012. Jurnal Gaussian is published by Department of Statistics, Faculty of Science and Mathematics, Diponegoro University. Jurnal Gaussian publishes scientific articles on various aspects related to statistics, probability, and its application. Articles can be in the form of research results, case studies, or literature reviews. This journal has been accredited by the National Journal Accreditation (ARJUNA) managed by The Ministry of Education, Culture, Research, and Technology, Republic of Indonesia with Third Rank (SINTA 3) from 2023 to 2027 according to SK Nomor: 74/E/KPT/2024. https://sinta.kemdikbud.go.id/journals/profile/8421 Publication Schedule: Starting in 2024 it is published every month of the year, with two numbers. The first number starts from February and the second number starts from August. Indexing: Dimension, SINTA, Google Scholar, BASE, GARUDA, and One Search Document at Scopus: Citation Tracker OAI address: https://ejournal3.undip.ac.id/index.php/gaussian/oai
Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro
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PEMODELAN REGRESI GAMMA MENGGUNAKAN METODE OPTIMASI BROYDEN-FLETCHER-GOLDFARB-SHANNO (BFGS) (Studi Kasus : Pencemaran Sungai di Kota Semarang)
Semarang City is one of the major industrial areas in Central Java and is located not far from residential areas. These large industries utilize a variety of chemicals to meet their needs, producing various wastes that are the main cause of high concentrations of Chemical Oxygen Demand (COD) in waters. Measurements on the COD value obtained are continuous data with Gamma distribution. In this study, Gamma regression is used to model the relationship between one or more predictor variables and a positive continuous response variable following a Gamma distribution. Parameter estimation in the Gamma regression model uses the Maximum Likelihood Estimation (MLE) method because it does not produce an analytical solution, an optimization method will be carried out with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. This study aims to determine the Gamma regression model in the case of river pollution in Semarang City, determine the form of parameter estimation in the Gamma regression model and get what factors affect river pollution in Semarang City. Based on the value of 0.4431498 where the ability of the predictor variables to explain the response variable is 44.32%, the remaining 55.68% of the response variable is explained by other factors not contained in the model.
PERAMALAN HARGA BERAS DI INDONESIA MENGGUNAKAN METODE HOLT-WINTERS ADDITIVE EXPONENTIAL SMOOTHING DENGAN OPTIMASI GOLDEN SECTION
Rice is one of the staples that must be fulfilled to support human survival. As a result, if the price of rice is instable, it can cause a decrease in people's purchasing power. Therefore, a system is needed that can forecast rice prices to help maintain food security. This study uses the Holt-Winters Additive method because it can be used to predict time series data that has trend and seasonal patterns. The optimum parameter is found using the Golden Section optimization method that minimize the MAPE value. The data used is the average monthly data of rice prices at the level of large trade (wholesale) Indonesia. The results showed that the data contained elements of trend and seasonality additives and obtained the best model with α = 0.999702, β = 0.059114, γ = 0.145618. The results of measuring the forecasting ability of the formed model show that the forecast results are close to the actual data and are evidenced by the MAPE out sample value of 7.006% which is include MAPE criteria < 10% so that the forecasting ability is very high. The forecast results for 2023 show that rice prices have fluctuated but the changes are not too significant.
PENERAPAN MODEL REGRESI RANDOM FOREST UNTUK PREDIKSI HARGA LAPTOP BERDASARKAN FITUR LAPTOP
The increasing use of computer science systems in various fields of work is driving the growth of laptop. There are many choices of laptop products with different specifications. Laptop price predictions can help consumers to find out the price range of laptops according to the laptop features they want. This study aims to apply the random forest regression method to predict laptop price based on laptop features. The data is splitted into 2 parts, 1130 data as training set and 283 data as testing set. Hyperparameters tuning was performed using random search CV with 10 fold cross-validation to find the combination of hyperparameters that produced the optimal model. The best hyperparameters obtained to build a random forest regression model are ntree = 400, mtry = 2, and nodesize = 2. The MAPE value of the testing set for the random forest regression model is 14,3% which indicates the performance of the model has good forecasting ability. The results of the analysis show that the random forest regression method can be applied to predict laptop prices based on laptop features. Based on the variable importance, the variable that has the greatest contribution to the laptop price prediction results is RAM with VI = 0,359.
Pengklasteran dan Penerapan Rantai Markov untuk Prediksi Produksi padi dan Lahan Panen di Kalimantan Barat
The population growth rate in Indonesia is very high. This causes the need for rice to also increase. The increase in population growth is not matched by the growth of harvested land. This causes the area of harvested land to decrease because a lot of land is converted into settlements. Rice production and harvest land in West Kalimantan has decreased in the period 2019 to 2021. The purpose of this study is to classify and predict rice production and harvest land in West Kalimantan. In this research, the clustering method used is Cluster Time Series with Average Linkage method. Average Linkage is one of the hierarchical groupings based on the average distance between objects. The Silhouette Coefficient value is used to determine the optimal number of clusters. This research also uses the Markov Chain method to predict rice production and harvestable land. Markov chain is a stochastic process that explains future events only depend on today's events and do not depend on past circumstances. The results of this study obtained two clusters and many districts/cities are in clusters that have low rice production and harvest land. The prediction results of rice production and harvested land in Kalimantan have the greatest chance of experiencing a decline.
Penerapan Metode Fuzzy Time Series Markov Chain Untuk Meramalkan Nilai Transaksi Belanja Menggunakan Uang Elektronik di Indonesia
Forecasting is an analytical process used to predict future conditions based on historical and current data to minimize errors. The Fuzzy Time Series (FTS) Markov Chain method is effective for handling uncertain, nonlinear, and fluctuating data, making it suitable for forecasting electronic payment transactions in Indonesia. These transactions often show gradual trends, seasonality, and external influences such as policy changes and consumer behavior, leading to data uncertainty that traditional models struggle to capture. A key factor in the FTS method is the interval length, which affects the accuracy of fuzzy set formation. This study compared two interval determination methods: Sturges formula and automatic clustering, to forecast Indonesia’s electronic payment transaction value for September 2024. Results showed that Sturges produced a forecast of Rp52,836.07 billion with a MAPE of 8.51%, while automatic clustering yielded a forecast of Rp55,369.31 billion with a lower MAPE of 3.90%. The findings indicate that the hybrid FTS-Markov Chain approach, especially when combined with automatic clustering, offers better accuracy. It adapts more effectively to the natural structure of the data, making it a more reliable method for forecasting complex and uncertain transaction patterns.
PENERAPAN MODEL REGRESI SEMIPARAMETRIK DERET FOURIER UNTUK MENGIDENTIFIKASI FAKTOR PENENTU ANGKA HARAPAN HIDUP DALAM KONTEKS SDGS 3
Semiparametric regression combines parametric and nonparametric regression, applied when some relationships between the response and predictor variables are known while others are unknown. This study employed linear regression for the parametric component and the Fourier series estimator for the nonparametric component. The data consisted of life expectancy in Indonesia and its influencing factors, relevant to Sustainable Development Goals (SDGs) 3. The relationship between life expectancy and some predictors (maternal mortality rate, poverty rate) was linear, whereas with others (open unemployment rate, average years of schooling, Gini ratio, stunting prevalence, exclusive breastfeeding) the pattern was unknown and tended to be periodic. This characteristic aligns with the strength of the Fourier series semiparametric regression, which combines linear modeling with Fourier series components for nonlinear periodic relationships. The objective was to determine the optimal number of oscillations using the Generalized Maximum Likelihood (GML) method, obtain the best model, and identify factors affecting life expectancy. Results showed the best model had three oscillations with a GML of , RMSEP of 0.99, and R² of 82.67%. Significant factors included poverty rate, open unemployment rate, average years of schooling, Gini ratio, stunting prevalence, and exclusive breastfeeding.
PERBANDINGAN PERFORMA MODEL ARIMA-GARCH DAN LSTM DALAM MERAMALKAN JUMLAH KUNJUNGAN WISATAWAN DANAU KASTOBA
Kastoba Lake, located on Bawean Island, East Java, is a unique natural tourist destination with significant potential for further development. To enhance strategic tourism management, predicting tourist visit numbers is necessary. This study aims to assess the performance of the ARIMA-GARCH and Long Short-Term Memory (LSTM) models in predicting daily tourist arrivals to Kastoba Lake, based on data collected between March 2023 and July 2024. These two methods were specifically selected because the dataset exhibits nonlinear patterns and heterogeneous variance. The ARIMA-GARCH model was employed to handle heteroscedasticity within the data, while LSTM was chosen for its ability to effectively learn and represent long-term patterns. The findings indicate that both models deliver comparable performance and are highly capable of identifying the underlying data trends. Moreover, each model is effective in forecasting short-term tourist visits, particularly over a 7-day horizon (one week). Consequently, these models are reliable tools for predicting and analyzing tourism trends at Kastoba Lake.
PEMODELAN ANGKA HARAPAN HIDUP DI INDONESIA DENGAN PENDEKATAN BAYESIAN: BAYESIAN ADAPTIVE SAMPLING DAN BAYESIAN MODEL AVERAGING DALAM SELEKSI VARIABEL
This study applies Bayesian Adaptive Sampling (BAS) and Bayesian Model Averaging (BMA) to model life expectancy in Indonesia, addressing model uncertainty and improving predictive accuracy. The analysis incorporates Zellner’s g-prior, which enhances variable selection by balancing prior information and data-driven learning, ensuring more stable and reliable parameter estimation. Bayesian methods provide greater flexibility compared to classical regression, particularly in managing heterogeneous demographic data. The results identify poverty rate, healthcare professional ratio per 1,000 residents, percentage of infants receiving exclusive breastfeeding, and regional health expenditure as key determinants of life expectancy. The poverty rate negatively impacts life expectancy, whereas the other factors contribute positively, highlighting the importance of healthcare access, infant nutrition, and government investment in public health. The final model achieves an R² of 78.1%, indicating that these variables collectively explain a substantial proportion of life expectancy variability. By integrating Zellner’s g-prior, Bayesian inference facilitates a robust selection of influential predictors, leading to more precise policy recommendations. The study suggests that enhancing healthcare distribution, promoting breastfeeding awareness, and optimizing health budget allocation can significantly improve life expectancy outcomes. Bayesian methods provide a powerful framework for demographic modeling by incorporating uncertainty and refining estimation accuracy.
PERBANDINGAN METODE OPTIMASI SILHOUETTE, ELBOW, DAN GAP STATISTICS DALAM MENENTUKAN NILAI K TERBAIK PADA ANALISIS K-MEANS CLUSTERING
Stunting is a condition of malnutrition status that is chronic in growth and development from the beginning of life, malnutrition puts children at greater risk of death. One of the efforts to overcome stunting is to determine in advance the provinces that need to be prioritized in handling the factors that cause stunting by grouping 34 provinces in Indonesia. This study uses k-means clustering to partition data according to their respective characteristics into the form of two or more clusters, determining the optimal number of clusters through elbow optimization methods, gap statistics and silhouette. The method used to test the best cluster results is the Davies Bouldin Index (DBI) method. The results of the elbow method clustering test produce K = 3 with a DBI value of 0.6392677, the gap statistics method produces K = 1 without DBI testing because only 1 cluster is formed, while the silhouette method produces K = 2 with a DBI value of 0.2116945. This shows that the results of clustering k-means with the silhouette method produce better cluster quality because it has a lower DBI value than other methods.
IMPLEMENTASI METODE CONVOLUTIONAL NEURAL NETWORK UNTUK KLASIFIKASI SENTIMEN ULASAN PENGGUNA APLIKASI MYPERTAMINA
Sentiment analysis has gained significant attention in recent years, with researchers employing various machine learning and deep learning techniques. While Convolutional Neural Networks (CNN) were initially designed for image processing, their effectiveness in text classification tasks has been established. This study focuses on enhancing sentiment classification performance for customer reviews of MyPertamina by utilizing a CNN model with Word2Vec embeddings. The research involves analyzing user reviews obtained from the Google Play Store for MyPertamina's mobile application. The CNN model, incorporating Word2Vec embeddings, is trained to classify these reviews into positive and negative sentiment categories. Experimental evaluations reveal that the optimal hyperparameters for the Word2Vec model are a window size of 5 and a word embedding dimension of 300. Regarding the CNN model, both the dropout rate and learning rate significantly impact classification performance. The best results are achieved with a learning rate of 0.001 and a dropout rate of 0.3. The findings demonstrate that the CNN model with Word2Vec embeddings achieves an impressive accuracy of 96.14% in classifying customer reviews within the MyPertamina application. This underscores the efficacy of employing this approach to improve sentiment classification for customer feedback.
COMPARATIVE ANALYSIS OF K-MEANS, K-MEDOIDS, AND FUZZY C-MEANS FOR CLUSTERING PROVINCES IN INDONESIA BASED ON RICE PRODUCTION IN 2024
Rice is one of the main commodities in Indonesia's agricultural sector that plays a crucial role in maintaining national food security. This study aims to cluster 38 provinces in Indonesia based on the similarity of rice production in order to understand the spatial variation of agricultural performance in different provinces. In this analysis, three clustering methods were used, namely K-Means, K-Medoids, and Fuzzy C-Means, by considering two main variables: the area of harvest and the amount of rice production in 2024, whose data were sourced from the Central Bureau of Statistics. Evaluation of cluster quality was conducted using the Davies-Bouldin Index (DBI). The results showed that the K-Means method produced the most optimal clustering with the lowest DBI value of 0.276 at the number of clusters , compared to K-Medoids (0.279 at ) and Fuzzy C-Means (0.285 at ). The clusters formed show a clear separation between provinces with high and low production levels. Provinces with high agricultural intensification and a large contribution to production belong to the main cluster, while areas with limited resources and low production form a separate cluster. Several other clusters reflect medium to high production characteristics with varying development potential. This finding reflects the diversity of agricultural conditions influenced by infrastructure, intensification, and geographical and climatic factors.
OPTIMALISASI PORTOFOLIO MENGGUNAKAN METODE MEAN-SEMIVARIANCE PADA SAHAM IDX30
Investment is one way to maximize income. Through investment, investors who invest funds will benefit. However, investment is inseparable from risk. Investors can reduce investment risk by forming an optimal portfolio. Mean-semivariance is one method of portfolio formation invented by Markowitz in 1959. Mean-semivariance is a mean-variance development method, but this method is free from all assumptions and this method measures portfolio risk by using semivariance and semideviation. The investment that many investors choose is a stock investment. This research uses stocks that have consistently joined the IDX30 for five years (2018-2022). IDX30 is composed of 30 stocks with relatively large market capitalization, high liquidity, and good fundamentals. The optimal portfolio is formed by calculating the weight of each stock using a function, so as to get the smallest risk. Based on the four optimal portfolios that are formed through the process, it is known that the optimal portfolio with the best performance is Portfolio 2. The Sharpe index belonging to Portfolio 2 is 0.083507. The investment weight for each share that makes up Portfolio 2 is 16.1039% for shares of PT Adaro Energy Indonesia Tbk; 57.5554% for shares of PT Indofood CBP Sukses Makmur Tbk; and 26.3407% for shares of PT Perusahaan Gas Negara Tbk.
PERBANDINGAN METODE HAZARD MULTIPLIKATIF DAN ADITIF PADA LAJU PERBAIKAN KONDISI KLINIS PASIEN STROKE DI RS MH THAMRIN CILEUNGSI TAHUN 2021
Stroke is a condition that can result in permanent brain damage or even death. In Indonesia, the prevalence of stroke increased from 7% in 2013 to 10.9% in 2018. Numerous factors can affect a stroke patient's ability to recover. Survival analysis is a method that can be used to identify the variables that influence stroke patient’s ability to recover. Cox proportional hazard and Lin-ying additive hazard approaches were utilized in this study to analyze stroke patient data from MH Thamrin Cileungsi Hospital. The most widely used regression model for survival data is the Cox proportional hazard which makes the assumption that the ratio between the hazard functions of various people is constant. In contrast, in additive hazard regression there is no assumption of proportionality. Age and cardiac history are the factors that have an impact on how well stroke patients recover, according to the findings. The Lin-Ying additive hazard approach yields the best results since its RMSE value is lower (0.3808777) than that of the cox proportional hazard model (0.9248512).
ANALISIS KUALITAS STANDARD STRENGTH PADA PORTLAND COMPOSITE CEMENT DENGAN METODE CONTROL CHART DAN EVALUASI KAPABILITAS PROSES PRODUKSI
The quality of cement products can be determined based on the results of standard strength tests, which are carried out using cube-shaped test samples through a compression testing machine. In the context of a continuously developing manufacturing industry, the demand for high-quality cement in Indonesia has also increased significantly. Therefore, it is necessary to implement production process control to ensure consistent quality that meets market needs. The main focus of the research is on evaluating process stability and the process's ability to meet standard strength specifications using the X-bar and R control chart methods and process capability calculations. The results show that process variability is under statistical control when viewed from the R control chart, but the process average is not under statistical control, as indicated by 8 out of 21 points outside the control limits on the X-bar control chart. These points were identified as variations due to common causes inherent in the process. Nevertheless, process capability analysis showed that the process was technically capable of meeting specifications, with a Cp value of 4.35. Therefore, it was concluded that the Standard Strength production system at the company was capable despite statistical variation in the process mean.
ANALISIS TINGKAT PENGANGGURAN TERBUKA BERDASARKAN INDIKATOR SOSIAL DI PROVINSI KEPULAUAN BANGKA BELITUNG MENGGUNAKAN PENDEKATAN REGRESI B-SPLINE
The Open Unemployment Rate (TPT) is usually an important indicator in assessing the level of effectiveness of regional development in providing employment. In the Bangka Belitung Islands Province, the dynamics of the TPT have shown a fluctuating pattern over the past few years. The fluctuation of the TPT can be caused by several social indicators such as the Labor Force Participation Rate (TPAK), the Gross Participation Rate (APK) of upper education, and the Poverty Depth Index (P1). Judging from the data obtained, the form of data that has an irregular pattern, the method used in this study is b-spline regression which can capture fluctuating patterns in the data. The results show that the b-spline model is very good at capturing fluctuating patterns in the Open Unemployment Rate with several other social indicators seen from the MAE value of 0.05879, RMSE of 0.081630 and Adjusted R-squared of 0.7206 indicating that the b-spline regression model is able to explain around 72.06% of the variation in the response variable. Based on the results of the simultaneous test, it shows that variable have a significant effect on TPT, while the partial test it shows APK SMA and P1 have a significant effect on TPT.
Efektivitas ECM - MIDAS berbasis Principal Component Analysis (PCA) dalam Memprediksi PDB di Indonesia
GDP is closely related to monetary policy, because changes in GDP often affect decisions taken by the central bank in formulating policies to maintain economic stability. This study aims to predict the value of Gross Domestic Product (GDP) by developing a more accurate and efficient model. The variables analyzed include primary money, net domestic assets, net foreign position, and foreign exchange reserves as independent variables, and gross domestic product (GDP) as the dependent variable. The method used combines the Error Correction Model (ECM) into the Mixed Data Sampling (MIDAS) and Principal Component Analysis (PCA) models, this approach provides a more comprehensive analytical framework to capture complex interactions between variables with different frequencies, while taking into account long-term and short-term dynamics that influence each other. The results of the study indicate that the combination approach of PCA and MIDAS with the Almon distribution is more effective in capturing data patterns than other approaches that only use PCA with the average or median of economic indicators. The ECM-MIDAS-PCA model with the Almon weight function showed the best results, marked by an Adjusted R-Square value of 22.33% and low prediction error. The Error Correction Term (ECT) coefficient of -0.1579 indicates a correction towards long-term equilibrium of 15.79% per quarter, so that the process towards equilibrium can be achieved in 6.33 quarters.
FUZZY POSSIBILISTIC C-MEANS (FPCM) CLUSTERING UNTUK IDENTIFIKASI KELUHAN UTAMA PELANGGAN INDIHOME PADA DATA TWEETS
Customer complaints reveal product or service issues and can drive improvements to enhance satisfaction. Many companies use Twitter as a platform to interact with customers, making handling complaints through social media crucial for building a positive image and maintaining customer loyalty. IndiHome Regional 4 faces challenges in identifying main complaints due to a high volume of complaints on Twitter. Cluster analysis groups similar complaints, aiding the identification process. Text mining converts textual data into numerical format, streamlining complaint processing. Fuzzy Possibilistic C-Means Clustering, a fuzzy-based method, enables data membership across clusters with varying degrees of membership. By adopting relative (fuzzy) and absolute (possibilistic) membership, more accurate data placement is achieved. Data consists of IndiHome Regional 4 customer complaint tweets received via the Twitter channel "IndiHomeCare" from January to December 2022. The clustering process formed 4 clusters based on the smallest Extended Xie-Beni Index value, tested with different cluster numbers (3-7). Witel Yogyakarta had the highest members and complaints in each cluster, while Witel Kudus had the lowest. Word Cloud analysis revealed main complaints in each cluster, including WiFi-related subscription costs, internet disruptions, customer service issues, and slow connections.
PEMODELAN JUMLAH KASUS KEMATIAN BAYI DAN IBU DI PROVINSI LAMPUNG MENGGUNAKAN BIVARIATE GENERALIZED POISSON REGRESSION
Maternal and infant mortality are closely related, as the fetus receives nutrition from the mother through the placenta. Therefore, the mother's health condition during pregnancy directly impacts fetal development. Additionally, the mother's role in caring for the infant significantly affects the child's growth and survival. One of the goals of the Lampung Provincial Health Office’s Regional Medium-Term Development Plan (RPJMD) for 2020–2024 is to reduce maternal and infant mortality. The expected health target by the end of 2024 is to lower maternal deaths to 110 cases and infant deaths to 520 cases. This study employs the Bivariate Generalized Poisson Regression (BGPR) method to identify factors influencing maternal and infant mortality in Lampung Province in 2022. BGPR is suitable for handling overdispersed count data with two correlated response variables. Based on the AICc criterion, the best model includes all prediktor variables. The results show that the percentage of deliveries assisted by health professionals (X1) significantly affects maternal mortality, while both the percentage of deliveries by health professionals (X1) and the percentage of fourth antenatal care visits (K4) (X3) significantly affect infant mortality.
PERBANDINGAN HUKUM MORTALITAS GOMPERTZ DAN MAKEHAM DALAM KONSTRUKSI TABEL MORTALITAS INDONESIA IV
Developing accurate mortality tables that reflect real conditions is a major challenge. Some researchers have proposed mortality laws using relatively simple equations that consider only age. Gompertz’s law accounts for the increasing risk of death with age, while Makeham’s law adds age-independent risk factors. This study aims to estimate the parameters of the probability of death function in both Gompertz and Makeham laws using the least squares method. The estimation process involves minimizing the squared error function of the mortality probability to form a normal equation. In this study, the resulting equation cannot be solved explicitly, a numerical approach using the Secant method is applied. The estimated parameters are then used to construct a mortality odds table, which is compared with data from the Indonesian Mortality Table IV. Model evaluation using the Mean Squared Error (MSE). The results of the analysis show that the Makeham model with the least squares method provides the best performance, indicated by the lowest MSE value of 0.0002002492 for men and 0.0003069904 for women. These findings indicate that the Makeham model outperforms the Gompertz model in constructing mortality tables using the least squares method.
IMPLEMENTASI METODE SUPPORT VECTOR REGRESSION UNTUK PREDIKSI HARGA SAHAM PT. ADARO ENERGY TBK
Stock investment is very attractive to investors because it provides many benefits. The higher the profit offered in investing, the higher the risk investors will face. Stock price analysis is needed to predict stock prices to reduce the risk of loss. Stock data has dynamic, non-linear, and unpredictable characteristics, so a method is required to overcome the limitations of time series data. The Support Vector Regression method will be applied in this study to predict PT. Adaro stock prices. The Support Vector Regression method is one method that does not require assumptions, so it can be used to overcome the limitations of regression analysis with time series data. The problem often faced when using the SVR method is determining the optimal hyperparameters. This study determines the optimal hyperparameter using the grid search algorithm. The data is divided into training and testing data with a ratio of 90:10. The best kernel to predict the share price of PT. Adaro is using a linear kernel with a value of Cost = 4 and epsilon = 0.0001. The model produces MAPE testing data of 1.608%, which means the model is very good for prediction.
PERAMALAN INDEKS HARGA SAHAM GABUNGAN (IHSG) DENGAN METODE FUZZY TIME SERIES CHEN DAN CHENG
The Jakarta Composite Index (JCI) is an index that measures the performance of all stocks listed on the Indonesia Stock Exchange. JCI can be used as one of the indicators used by investors to determine the movement of stocks in the Indonesian capital market. Decisions made by investors will have a stronger basis if forecasting is done. Investors can decide to exit the market or enter the market. The forecasting method used to forecast the JCI value in this study is Fuzzy Time Series (FTS). This method has advantages compared to other time series methods, where the FTS method does not require the fulfillment of classical assumptions as in ARIMA. Both forecasting methods will apply the Sturges and Average Based formulas in determining the class. The data used in this study is the JCI closing data on March 1, 2022 - March 1, 2023. The data is divided into two categories with 239 data as training data, namely data on March 1, 2022 - February 15, 2023 and 10 data as testing data, namely data on February 16 - March 1, 2023. The forecasting accuracy measure used in this study is sMAPE. Among the four forecasting methods, the best forecasting method is Cheng's Fuzzy Time Series method by applying the Sturges formula in determining the number of classes with an sMAPE value on testing data is 0.37%.
ANALISIS KEMISKINAN, KETIMPANGAN, DAN PENGANGGURAN TERHADAP IPM DI 3 PROVINSI SUMATERA MENGGUNAKAN SPLINE TRUNCATED
This study aims to analyze the effect of the open unemployment rate (TPT), economic inequality (Gini ratio), and the percentage of poor people on the Human Development Index (HDI) in three provinces with the highest poverty rates on Sumatra Island, namely Aceh, Bengkulu, and South Sumatra. The truncated spline nonparametric regression method was used in this study to accommodate the complex relationship between variables without assuming a particular distribution. The results of the analysis show that all three independent variables have an effect. The results of the analysis show that the best model is obtained with four knot points, producing a minimum Generalized Cross Validation (GCV) value of 7,9580594, a minimum Mean Squared Error (MSE) value of 3.899, and a coefficient of determination (R²) of 77,96%. With a fairly high level of accuracy, this model can be used as a basis for further analysis in understanding the relationship between economic variables and the HDI. In addition, this model can be a reference in formulating more effective policies to reduce economic inequality and improve the welfare of people in the poorest areas on Sumatra Island.
PENGKLASIFIKASIAN PENYAKIT HIPERTENSI MENGGUNAKAN METODE CHI-SQUARE AUTOMATIC INTERACTION DETECTION
Data mining is a technology used as an automated tool in the decision-making with classification being one of its techniques. The Chi-square Automatic Interaction Detection method classifies data by dividing samples into groups based on certain criteria, displaying results in a tree diagram. This study aims to obtain related factors, classification results, and accuracy of hypertension status classification of visitors to the East Kalimantan Provincial Health Office stand at the 2023 Kaltim Expo in Samarinda City using the CHAD method. The study found that age and family history are factors related to hypertension status. Classification results showed 10 elderly visitors without a family history of hypertension (2 with hypertension, 8 without), 216 non-elderly visitors without a family history of hypertension (9 with hypertension, 207 without), 10 elderly visitors with a family history of hypertension (9 with hypertension, 1 without), and 117 non-elderly visitors with a family history of hypertension (36 with hypertension, 81 without). The accuracy of hypertension status classification using the CHAID method was 86%.
PERFORMA PREDIKSI: KOINTEGRASI GARCH-SVR VS. GARCH UNTUK VOLATILITAS HARGA KOMODITAS ENERGI GLOBAL
Forecasting provides benefits in decision-making, one of which is forecasting the volatility of global energy commodity prices. However, there are challenges in forecasting volatility due to the presence of heteroskedasticity and long-memory effects in the data. Therefore, a combination of the GARCH and SVR methods is needed as a cointegration-based machine learning approach. The aim of this study is to compare the forecasting performance of GARCH and GARCH-SVR for global energy commodity price volatility. The findings indicate that the GARCH-SVR model performs well when volatility data exhibits non-stationary long-memory characteristics, whereas the GARCH model is more suitable when the volatility data shows stationary long-memory characteristics.
BOOTSTRAP AGGREGATING CLASSIFICATION AND REGRESSION TREES (BAGGING CART) UNTUK KLASIFIKASI POTENSI KARYAWAN RESIGN BERDASARKAN KENYAMANAN BEKERJA
Phenomenon of employee resignation is a significant challenge for companies because it affect the productivity and stability of the company's operations. Every companies supposed to analyze the potential of employee resignation. This research aims to classify the potential of employee resignation based on working comfort and applies the classification modeling method from Decision Tree: Classification And Regression Trees (CART) and the ensemble Bootstrap Aggregating (Bagging) method. CART is a non-parametric method that is effective in building classification and prediction models based on decision trees, while Bagging is an ensemble method that combines several CART models to improve the accuracy and stability of predictions. The CART model provides an accuracy of 73% and f1-score of 62%, while the Bagging CART model provides an accuracy of 87% and f1-score of 88%. This research shows an increase in accuracy when using Bagging CART model of 14%. The most important variable to build the model and make predictions is the age. Age is also used as the root node in building CART model.
AKURASI KINERJA METODE HYBRID GEOMETRIC BROWNIAN MOTION-KALMAN FILTER DALAM PERAMALAN HARGA SAHAM INDONESIA
This study aims to analyse the performance of a stock price forecasting model based on Geometric Brownian Motion (GBM) modified with the Kalman Filter (KF) approach. The GBM model is used to represent the basic behaviour of stock price movements, which are stochastic in nature, while the Kalman Filter plays a role in estimating model parameters based on actual observation data. This study uses closing price data for PT. Aneka Tambang Tbk. (ANTM) shares. The results of this study show the accuracy level using Mean Absolute Error Percentage (MAPE) in the GBM-KF hybrid model and are in the best fitting condition. For ANTM shares, it is 5.72% (GBM) and 3.83% (Hybrid GBM-KF). The GBM-KF hybrid model has proven to be effective in minimising prediction errors and capturing changes in market trends and volatility that cannot be explained by the classic GBM model. Furthermore, this study highlights that integrating Kalman Filter into GBM improves the model’s adaptability to dynamic market conditions, allowing for real-time parameter estimation and enhanced predictive stability. The findings suggest that the GBM-KF framework can serve as a robust tool for financial forecasting, particularly in volatile markets where traditional models tend to underperform.
PENERAPAN MODEL AUTOREGRESSIVE FRACTIONALLY INTEGRATED MOVING AVERAGE DALAM MERAMALKAN NILAI TUKAR RUPIAH TERHADAP US DOLLAR (USD/IDR)
The Autoregressive Fractionally Integrated Moving Average (ARFIMA) model is employed to analyze data exhibiting long memory characteristics using a fractional differencing coefficient. This study differs from previous research, as no existing studies have been found that discuss the forecasting of the rupiah exchange rate against the United States Dollar (USD) using recent data and the ARFIMA model. This study examines the daily exchange rate of the Rupiah against the United States Dollar (USD/IDR) from January 2023 to March 2025, totalling 535 observations. The results indicate a general weakening trend of the Rupiah during this period. The Hurst exponent (H = 0.8372489), which falls within the range 0.5 < H < 1, confirms the presence of long memory properties. The best fitting ARFIMA model is identified as ARFIMA(2,0.3372489,1), with a BIC value of 4387.69. The model equation is: . Forecasting results show a downward trend, suggesting potential appreciation of the rupiah against the USD in the future. These findings provide valuable insights into exchange rate dynamics and have important implications for economic planning and policy in Indonesia.
OPTIMASI PORTOFOLIO CAPITAL ASSET PRICING MODEL (CAPM) PADA INDEKS BISNIS-27
Stock efficiency analysis helps investors understand the intrinsic value of a stock and serves as a foundation for identifying risk factors and potential returns associated with it. This study evaluates stocks in the Business Index 27 from 22 Mei 2023 – 22 Mei 2024 by considering criteria such as positive returns, lowest correlation, and sectoral differences. Based on this evaluation, three stocks with efficient performance were selected: MEDC, BRPT, and JSMR. An optimal portfolio was formed by weighting these three stocks using the Capital Asset Pricing Model (CAPM) method, with weight proportions of MEDC at 23.3%, BRPT at 11.7%, and JSMR at 64.9%. Risk evaluation using the Historical Simulation method to calculate Value at Risk (VaR) indicates a potential loss of 10%. This study provides insights into identifying efficient stocks and forming an optimal portfolio, which can assist investors in making investment decisions in the Business Index 27.
PERBANDINGAN REGRESI NONPARAMETRIK SPLINE TRUNCATED DAN KERNEL GAUSSIAN DALAM MENGANALISIS FAKTOR-FAKTOR PENENTU INDEKS PEMBANGUNAN MANUSIA (IPM) DI INDONESIA
The Human Development Index (HDI) is an important indicator for measuring the quality of development in a region. This study compares two nonparametric regression approaches, namely truncated spline regression and Gaussian kernel regression, in analyzing the factors influencing HDI in Indonesia in 2024. The independent variables used include Expected Years of Schooling (HLS), Mean Years of Schooling (RRLS), and the percentage of the poor population (PPM). Nonparametric regression is chosen for its ability to capture complex relationships between variables without strict linearity assumptions. The results show that both methods effectively model the relationship between the variables and HDI. Truncated spline regression performs better in detecting structural changes, while kernel regression is more flexible in capturing smooth relationships. Model evaluation using the coefficient of determination (R²) and mean squared error (MSE) indicates that truncated spline yields an R² of 92.79% and an MSE of 1.8617, while Gaussian kernel regression results in an R² of 82.25% and an MSE of 3.6837. Therefore, truncated spline regression proves to be more accurate in modeling the relationship between determining factors and HDI, and it can serve as a more suitable alternative for analyzing complex and nonlinear patterns in human development policy research.
EVALUASI MODEL KLASIFIKASI DALAM DETEKSI PENIPUAN TRANSAKSI: STUDI KASUS PADA DATA TIDAK SEIMBANG
The rise in digital transactions increases the risk of credit card fraud, highlighting the need for a smart and accurate detection system. This study aims to develop a classification model that can effectively detect fraudulent transactions, despite data imbalance challenges. Data processing involves the use of the SMOTE technique to improve the representation of minority classes and Optuna for hyperparameter tuning. Three machine learning models are applied: Logistic Regression, Random Forest, and XGBoost. Model performance is evaluated using precision, recall, f1-score, and ROC-AUC. The results show that Random Forest achieves the best performance, with a precision of 0.91, recall of 0.74, and f1-score of 0.82. Logistic Regression achieves high recall but very low precision, while XGBoost produces a competitive AUC but a lower f1-score than Random Forest. This research highlights the importance of algorithm selection, data balancing with SMOTE, and parameter tuning to build an effective and adaptive fraud detection system for imbalanced data
Pemilihan Parameter Osilasi Optimal Menggunakan Generalized Cross-Validation (GCV) pada Regresi Nonparametrik Deret Fourier
This research focuses on determining the optimal oscillation parameter in a Fourier series nonparametric regression model using the Generalized Cross-Validation (GCV) method to analyze factors influencing poverty in Central Java Province in 2024. The response variable is the percentage of the poor population, with Gross Regional Domestic Product (GRDP), Average Length of Schooling (ALS), and Open Unemployment Rate (OUR) as predictor variables. The optimal model is selected based on the minimum GCV value, with performance evaluated using MSE and . The results show that the minimum GCV is achieved at one oscillation, yielding an MSE of 4.545 and an of 0.546, indicating that 54.6% poverty variation is explained by the predictors. Simultaneous testing shows a significant joint effect of predictors, while partial testing indicates no individual significance. Thus, GCV effectively determines the optimal oscillation parameter in Fourier series nonparametric regression for poverty analysis.
Estimator Campuran Spline Truncated dan Deret Fourier dalam Regresi Nonparametrik Untuk Data Kategori
Nonparametric regression analysis is ideal when data patterns are uncertain because the approach is highly flexible. In some nonparametric cases, each predictor variable exhibits a different form of association with the response variable. Using only one estimator may result in estimates that do not align with the actual data patterns. Therefore, a mixed estimator approach is needed to overcome this problem. This research introduces a truncated spline and Fourier series mixed estimator, in which the relational structure between the response and predictor variables changes across certain intervals, while others demonstrate a recurring pattern. However, most studies on nonparametric regression still use response variables expressed as quantitative data, even though there are conditions where the response variables are categorical data. Therefore, this study will develop a mixed estimator for categorical data. This study aims to obtain truncated spline and Fourier series mixed estimators in nonparametric regression for categorical data using the Maximum Likelihood Estimation method followed by Newton Raphson iteration. This study produces parameter estimators in mixed models by combining truncated spline functions and Fourier series functions in binary categorical data using the Newton Raphson iteration approach.
ANALISIS SISTEM ANTREAN DENGAN METODE BAYESIAN
Along with the times, the transportation sector has progressed quite rapidly. In connection with the transportation sector, a phenomenon that is easily found in everyday life is the queue at public transportation facilities. One of them is at the transportation facility at the airport. At the airport the queue that occurs is due to the large number of aircraft that come to get service from airport service facilities. However, the queue can be minimized with a good system. The purpose of this research is to find out changes or additional information from aircraft services, get a queue system model, and find out whether the service at the airport is good or not. The Bayesian method is used to combine prior information from previous research data (Widiawati, 2010) and current observed data (samples) to obtain updated information. The sample distribution (Weibull and inverse Gaussian) of the current observed data and the prior distribution (inverse Gaussian and Weibull) obtained from the prior information in the previous research data (Widiawati, 2010). The prior distribution and the likelihood function of the sample distribution are combined to obtain the posterior distribution. After calculating the posterior distribution, it is found that the model of the aircraft queue at Adi Soemarmo International Airport - Surakarta is (GAMMA/GAMMA/3): (GD/∞/∞) with steady state conditions already met (ρ<1) and based on the results of the performance measure of the aircraft queue system at Adi Soemarmo International Airport has a good condition.
PENERAPAN METODE ADAPTIVE BOOSTING (ADABOOST) PADA DECISION TREE UNTUK ANALISIS SENTIMEN PELANGGAN MAXIM
Information technology is currently growing rapidly, one form of technology beneficiary is using the internet, namely online transportation services based on mobile applications. Maxim is one of the online transportation services in Indonesia that offers relatively cheaper prices compared to other online transportation services. This study aims to apply the Adaptive Boosting (Adaboost) method with Decision Tree to classify Maxim's customer review data so that it can establish customer satisfaction factors. Review data was obtained from June – December 2022 with a total of 1500 reviews. Classification was carried out using the Adaptive Boosting method with a Decision Tree and Tuning Hyperparameter Grid Search. Adaptive Boosting is used to improve the performance of the Decision Tree so it can work better. The Grid Search algorithm is used to determine the best hyperparameter combination in Adaptive Boosting so that the classification process can be more optimal. Classification using the Adaptive Boosting model with Decision Tree yields accuracy, precision and recall values of 83,69%, 86,75% and 85,71% with the best parameter combination based on Grid Search is n_estimator (number of trees) 300 and learning rate 0,001. Based on this accuracy value, it can be concluded that the Adaptive Boosting model is quite good at classifying Maxim's customer review data.
Pemilihan Bandwidth Optimal pada Regresi Nonparametrik Kernel Menggunakan Metode Unbiased Risk (UBR)
Nonparametric regression is used when the relationship pattern between the response and predictor variables is not clearly defined. Among several nonparametric regression approaches, the kernel method is commonly used. The selection of the optimal bandwidth is a key factor in kernel regression since it significantly affects the estimation accuracy. The optimal bandwidth selection can be obtained using the Unbiased Risk (UBR) method. The study aims to derive the mathematical formulation of the UBR method and evaluate its effectiveness in determining the optimal bandwidth for Indonesia’s 2024 economic growth rate data. The results indicate that the UBR method can be utilized in choosing the optimal bandwidth in nonparametric kernel regression for the economic growth rate data in Indonesia in 2024, producing bandwidths for each predictor of , and , with a minimum UBR of 2.827 and an MSE of 2.198. This implies that the nonparametric regression model with the optimal bandwidth obtained using the UBR method has good predictive capability with a relatively low estimation error for the economic growth rate data in Indonesia.
Estimasi Probit Biner Semiparametrik Spline Truncated pada Status Persentase Penduduk Miskin
Regression analysis is a statistical method used to model the relationship between predictor variables and response variables. To analyse categorical response variables, probit regression can be used. There are three probit models based on the type of response variable, namely binary probit, multinomial probit, and ordinal probit. Binary probit is a method used to analyse response variables with two categories. Probit models are often used because they produce more stable probabilities in small samples because it uses the normal distribution. There are three types of binary probit models based on curve approaches, namely parametric, non-parametric, and semi-parametric. Semi-parametric regression was chosen because it combines parametric and non-parametric components. Conventional semi-parametric regression often cannot provide accurate estimates. Therefore, the use of truncated splines is relevant because they can handle the flexibility of unknown functions. This study aims to estimate a semi-parametric binary probit model with truncated splines using maximum likelihood estimation. The resulting likelihood function is not in closed form, requiring Newton-Raphson numerical iteration. The results show that the best model is obtained with one knot point, which has an accuracy of 84.21% and an AUC of 0.84, indicating that the model's prediction classification is verry good.