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Desak Putu Eka Nilakusmawati
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E-Jurnal Matematika
Published by Universitas Udayana
ISSN : -     EISSN : 23031751     DOI : https://doi.org/10.24843/MTK
Core Subject : Education,
Mathematics
The scope of the E-Jurnal Matematika includes analysis, algebra, topology, graphics, numerical simulation approaches or what is known as numerical analysis, optimal control, queuing problems, optimization, finance, biomathematics, industrial mathematics, financial mathematics, and others.
Arjuna Subject : Matematika - Matematika Terapan
Articles 10 Documents
 1 
PERAMALAN DURASI ETHEREUM MENGGUNAKAN MODEL AUTOREGRESSIVE CONDITIONAL DURATION I WAYAN SUMARJAYA; RENOVAR JOJOR DELIMA SIMANULLANG; RATNA SARI WIDIASTUTI
E-Jurnal Matematika Vol. 14 No. 3 (2025)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2025.v14.i03.p484

Abstract

Forecasting is the process of estimating future events using past data. Financial time series forecasting often prioritizes stock price variables. Apart from the stock price variable, inter-transaction time or duration is also an important variable to predict, because the timing of changes in financial prices cannot be predicted. Duration modeling and forecasting can be done using the autoregressive conditional duration (ACD) model. In this research, modeling and forecasting using the ACD model was carried out on Ethereum. This research aims to predict the duration of Ethereum in order to help traders know the time needed to reach the next price change. Several ACD models with four distributions, i.e., exponential, Weibull, Burr, and generalized gamma were fit to the Ethereum duration. The research results suggest that the Burr-ACD model produces the smallest AIC value compared to other distributed ACD models. However, the forecast results using the Burr-ACD models show increasing duration and hence are less accurate. The generalized gamma-ACD (2,2) model was then chosen as an alternative for forecasting Ethereum duration, showing that Ethereum duration forecast results are less than one second, which indicates the high frequency of transactions that occur on Ethereum.
ANALISIS VOLATILITAS DAN PERAMALAN KURS JUAL RUPIAH TERHADAP RIYAL ARAB SAUDI MENGGUNAKAN MODEL ARCH/GARCH ROSSY NOVIYANA; ADAWIYAH ASTI KHALIL
E-Jurnal Matematika Vol. 14 No. 3 (2025)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2025.v14.i03.p486

Abstract

Exchange rate volatility is a phenomenon that affects economic stability, particularly in the context of international trade between Indonesia and Saudi Arabia. This research aims to analyze the volatility of the Rupiah selling rate against the Saudi Riyal and to forecast the exchange rate using the ARCH/GARCH modeling approach. This research employs daily secondary data obtained from the official website of Bank Indonesia for the period from May 2023 to July 2025. The analysis includes stationarity testing, differencing transformation, ARIMA modeling, heteroskedasticity testing, and the application of the ARCH/GARCH model. The best ARIMA model, based on the Akaike Information Criterion (AIC), is AR(2) AR(7) I(1) MA(2) MA(7). The Lagrange Multiplier (LM) test indicates the presence of heteroskedasticity, necessitating the use of the ARCH/GARCH model. Among several alternatives, the GARCH(2,1) model is selected as the best model due to its highest log-likelihood value, lowest AIC, and successful second LM test confirming the absence of residual heteroskedasticity. The GARCH(2,1) model demonstrates strong forecasting performance with an RMSE of 15.51, MAE of 11.38, Theil’s U2 of 0.98, and a covariance proportion of 0.994. Overall, this model is suitable as a forecasting tool for the Rupiah selling rate against the Riyal in the future.
PENCARIAN LINTASAN TERPENDEK DENGAN ALGORITME DIJKSTRA DAN MINIMUM SPANNING TREE DENGAN ALGORITME SOLLIN TERHADAP PERJALANAN WISATA SEJARAH DI KABUPATEN SUMENEP LIKA HANIFA; LUH PUTU IDA HARINI; G.K. GANDHIADI
E-Jurnal Matematika Vol. 14 No. 3 (2025)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2025.v14.i03.p485

Abstract

A graph is a diagram that contains specific information.  One concept in graphs that can solve real-life problems is the concept of trees, which consists of various types of trees used to solve problems in life, such as finding the minimum path using the Dijkstra algorithm and the use of minimum spanning trees using the Sollin algorithm. This research produced the minimum path using Dijkstra's Algorithm and the minimum spanning tree using Sollin's Algorithm, which were applied to historical tourist routes in Sumenep Regency.
PERHITUNGAN PREMI BULANAN ASURANSI DANA PENSIUN MENGGUNAKAN METODE AGGREGATE COST PADA ASURANSI JIWA SEUMUR HIDUP MIA NUR FATAYATIN; I NYOMAN WIDANA; DESAK PUTU EKA NILAKUSMAWATI
E-Jurnal Matematika Vol. 14 No. 3 (2025)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2025.v14.i03.p489

Abstract

Pension insurance is a long-term financial program managed by an official institution. The premium, as the participant’s mandatory contribution, is determined by the type of product and the annuity chosen. Monthly premiums in a pension program play an important role in ensuring that participants receive benefits once they reach retirement age. This study aims to explain how monthly premiums are calculated using the Aggregate Cost Method in pension insurance programs. This method is chosen because it takes into account the participant’s average salary during their working years. The calculation is carried out by estimating all future benefit payments, which are then discounted using an assumed interest rate and survival probabilities based on mortality assumptions. The research uses data from employees who started working at the ages of 22, 25, and 30, in order to show how the entry age affects the amount of monthly premiums. The results indicate that both the monthly premium and the retirement benefits vary depending on the age at which the participant begins contributing. The earlier a person starts paying premiums, the lighter the financial burden they carry.
PERAMALAN PENGGUNAAN LISTRIK DI PROVINSI BALI MENGGUNAKAN METODE ARIMA I GEDE GANA ARIAWAN; I WAYAN SUMARJAYA; MADE SUSILAWATI
E-Jurnal Matematika Vol. 14 No. 3 (2025)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2025.v14.i03.p487

Abstract

This study aims to forecast electricity consumption in the Province of Bali using the ARIMA (Autoregressive Integrated Moving Average) method. The forecasting process is based on monthly electricity usage data spanning from January 2015 to June 2024. The initial analysis revealed a significant upward trend, with a notable decline in usage during 2020, coinciding with the COVID-19 pandemic. To address the issue of non-stationarity in the data, a differencing process was applied until stationarity was achieved, as confirmed by the Augmented Dickey-Fuller (ADF) test. Model identification was conducted using ACF and PACF plots, and several ARIMA models were evaluated based on their Akaike Information Criterion (AIC) values. The ARIMA(0,1,1) model was selected as the most suitable model due to its lowest AIC value and its compliance with diagnostic assumptions, including uncorrelated residuals (verified by the Ljung-Box test) and normally distributed residuals (confirmed by the Shapiro-Wilk test). The forecasting results demonstrated that the selected model provides stable predictions for the subsequent 12 months. This study is expected to contribute to effective planning and management of electricity demand in the Bali region.
PENENTUAN KINERJA PORTOFOLIO PADA SAHAM INVESTOR33 MENGGUNAKAN METODE GARCH DAN EWMA BERBASIS PADA INDEKS SHARPE ULFA MAULIDA; KOMANG DHARMAWAN; DESAK PUTU EKA NILAKUSMAWATI
E-Jurnal Matematika Vol. 14 No. 3 (2025)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2025.v14.i03.p488

Abstract

Assessing stock portfolio peirformancei is a cruicial steip in deiteirmining an optimal inveistmeint strateigy. This stuidy aims to analyzei thei peirformancei of thei Inveistor33 stock portfolio uising thei GARCH (Geineiralizeid Auitoreigreissivei Conditional Heiteiroskeidasticity) and EiWMA (Eixponeintially Weiighteid Moving Aveiragei) volatility eistimation meithods, which arei thein evaluated uising thei Sharpei indeix as a risk-to-reituirn indicator. Thei daily stock pricei data uiseid comeis from 33 seileicteid stocks activeily tradeid on thei Indoneisia Stock Eixchangei duiring a speicific obseirvation peiriod. Thei volatility eistimateis from both meithods arei uiseid to calcuilatei risk-adjuisteid portfolio reituirns. Thei Sharpei indeix is thein applied to asseiss thei portfolio's eifficieincy in geineirating reituirns reilativei to thei volatility eincouinteireid. Thei stuidy findings indicatei a significant diffeireincei in portfolio peirformancei beitweiein thei reisuilts calcuilateid uising thei GARCH and EiWMA meithods, with thei GARCH meithod teinding to providei morei accuiratei volatility eistimateis in volatilei markeit conditions. Thuis, thei choicei of volatility eistimation meithod significantly influieinceis risk asseissmeint and inveistmeint deicisions baseid on thei Sharpei indeix.
PCR DAN PLSR ALGORITMA NIPALS DALAM MENANGANI MULTIKOLINIERITAS PADA PREVALENSI STUNTING DI NUSA TENGGARA TIMUR NATALIE EFRATA SUSANTI; VERA MAYA SANTI; DEVI EKA WARDANI
E-Jurnal Matematika Vol. 14 No. 4 (2025)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2025.v14.i04.p491

Abstract

Nutritional problems contribute to 50% of deaths among children under five, particularly in low- and middle-income countries. One of the most common issues in Indonesia is stunting, a condition where a child's height falls below the standard for their age. In 2022, East Nusa Tenggara (NTT) recorded the highest stunting prevalence in Indonesia at 35.3%. However, quantitative statistical analyses of its contributing factors in NTT remain limited. This study aims to compare partial least squares regression (PLSR) using the NIPALS algorithm with principal component regression (PCR) in addressing multicollinearity. The secondary data were obtained from the 2022 Indonesian Nutrition Status Survey (SSGI), published by the Ministry of Health and BPS NTT, consisting of one response variable and ten predictor variables. Results showed that the PLSR model outperforms PCR, with an adjusted R² of 0.741 compared to 0.322. The superiority of PLSR is also evident from its lower RMSE and MAE values (2.783 and 1.910) compared to PCR (4.742 and 3.346). PLSR identified five significant predictors: average daily protein consumption per capita, number of children receiving DPT and HB immunizations, Human Development Index, percentage of households with access to safe drinking water, and number of people living in poverty.
ESTIMASI VALUE AT RISK PORTOFOLIO VALUTA ASING PADA KONDISI PANDEMI COVID-19 MENGGUNAKAN COPULA ANJAR ANGGRAINI; KOMANG DHARMAWAN; I WAYAN SUMARJAYA
E-Jurnal Matematika Vol. 14 No. 4 (2025)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2025.v14.i04.p490

Abstract

The Coronavirus disease (Covid-19) has been officially declared a pandemic by the World Health Organization (WHO). This pandemic affects not only the health of the population but also weakens the rupiah exchange rate. Fluctuations in exchange rate changes can affect the investment value, so investors need to take risk measurements. This study discusses the measurement of portfolio loss risk which is composed of a combination of USD, JPY, GBP, and EUR currency exchange rates using the value at risk (VaR) risk measure. Dependent structure analysis was carried out using the Gumbel, Clayton, and Frank copulas approach from the Archimedean copula family. The results obtained from this study are based on portfolio calculations composed of USD-GBP, JPY-GBP, and EUR-USD currency exchange rates at , , and  confidence levels in the next one-day period. The highest VaR of  is achieved by the EUR-USD portfolio at a  confidence level using the Gumbel copula. Meanwhile, the lowest estimated VaR of  is achieved by the EUR-USD portfolio at a  confidence level using the Gumbel copula.
ANALISIS KUANTITATIF KECELAKAAN LALU LINTAS DI AMERIKA SERIKAT PADA TAHUN 2000-2023 MENGGUNAKAN STATISTICAL QUALITY CONTROL IDA AYU OKTAVIANTI; ZAKIA ALYA ALYA ROSYDA; KEZIA BRILLIANT NAZARENA; NI WAYAN RUSNIATI; MADE AYU DWI OCTAVANNY
E-Jurnal Matematika Vol. 14 No. 4 (2025)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2025.v14.i04.p493

Abstract

Traffic accidents are a critical issue in road safety and public health in the United States. This study examines the patterns and statistical stability of annual traffic accidents from 2000 to 2023 using a Statistical Quality Control (SQC) approach. Secondary data were obtained from official publications of the National Highway Traffic Safety Administration (NHTSA), including accident severity, numbers of fatalities and injuries, population size, and risk indicators. The analysis employed five of the seven basic SQC tools, namely check sheets, histograms, Pareto diagrams, control charts (p-charts and u-charts), and cause-and-effect diagrams. The results show that property damage only accidents dominate total crash occurrences, while fatal crashes represent a small proportion but lead to significant loss of life. Control chart analysis indicates statistical instability in the proportion of fatal crashes and fatality rates, suggesting the presence of special causes rather than random variation. Overall, the findings highlight the usefulness of SQC as an effective tool for monitoring traffic safety performance and identifying critical variations requiring targeted interventions.
ANALISIS PENGENDALIAN CACAT PRODUK TELUR AYAM MENGGUNAKAN STATISTICAL QUALITY CONTROL DI BRAM FARM EVA KOSASIH; ALEN VIKTORIA BRIA; NI NYOMAN AYU NIRMALA LUKITA; NI PUTU SINTYA ARTA DEWI; MADE AYU DWI OCTAVANNY
E-Jurnal Matematika Vol. 14 No. 4 (2025)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2025.v14.i04.p492

Abstract

This study aims to analyze the quality control of chicken egg production at Bram Farm by applying Statistical Quality Control (SQC) tools to identify the level and types of defects that occur during the production process. Quantitative data were obtained from primary documentation through daily records collected over a 14-day observation period, consisting of the total number of eggs produced and the number of defective eggs categorized into specific defect types. Qualitative data were collected through direct observations and unstructured interviews with the farm owner to validate statistical findings and explore operational factors causing defects. The analysis employs three main SQC tools: the check sheet to record defect occurrences, the Pareto diagram to identify dominant defect categories, and the p-chart to evaluate the statistical stability of the production process. The results show that cracked eggs, thin-shelled eggs, and broken eggs are the dominant defects contributing to the overall defect rate. The p-chart indicates that all daily defect proportions fall within the control limits, demonstrating that the production process was statistically stable. These findings suggest that quality control at Bram Farm is effective, although improvement efforts should focus on the dominant defect categories to enhance production quality further.

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