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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 6 Documents
 1 
Search results for , issue "Vol. 14 No. 3 (2025)" : 6 Documents clear
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.

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