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Jambura Journal of Mathematics

jjom
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Published by Universitas Negeri Gorontalo

ISSN : 26545616 EISSN : 26561344 DOI : https://doi.org/10.34312/jjom

Core Subject : Education,

Mathematics

Jambura Journal of Mathematics (JJoM) is a peer-reviewed journal published by Department of Mathematics, State University of Gorontalo. This journal is available in print and online and highly respects the publication ethic and avoids any type of plagiarism. JJoM is intended as a communication forum for mathematicians and other scientists from many practitioners who use mathematics in research. The scope of the articles published in this journal deal with a broad range of topics, including: Mathematics; Applied Mathematics; Statistics; Applied Statistics.

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Articles 99 Documents

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Pendugaan Imbal Hasil Saham dengan Model Autoregressive Moving Average Grifin Ryandi Egeten; Berlian Setiawaty; Retno Budiarti
Jambura Journal of Mathematics Vol 3, No 2: July 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

ABSTRAKSeorang investor pada umumnya berharap untuk membeli suatu saham dengan harga yang rendah dan menjual saham tersebut dengan harga yang lebih tinggi untuk memperoleh imbal hasil yang tinggi. Namun, kapan waktu yang tepat melakukannya menjadi tantangan tersendiri bagi para investor. Oleh sebab itu, dibutuhkan suatu model yang mampu menduga imbal hasil saham dengan baik, salah satunya adalah model autoregressive moving average (ARMA). Tujuan dari penelitian ini adalah untuk menerapkan model autoregressive (AR), model moving average (MA), atau model autoregressive moving average (ARMA) pada data observasi untuk menduga imbal hasil saham bank central asia (BCA). Terdapat empat prosedur dalam membangun sebuah model AR, MA atau ARMA. Pertama, data yang digunakan harus weakly stationary. Kedua, orde dari model harus diidentifikasi untuk memperoleh model yang terbaik. Ketiga, parameter setiap model harus ditentukan. Keempat, kelayakan model harus diperiksa dengan melakukan analisis residual untuk memperoleh model yang terbaik. Pada akhirnya, model ARMA (1,1) adalah model terbaik dan akurat dalam menduga imbal hasil saham BCA. ABSTRACTGenerally, investor always wish to be able to buy a stock at a low price and sell it at a higher price to obtain high returns. However, when is the best time to buy or sell it is a challenge for investor. Therefore, proper models are needed to predict a stock return, one of them is autoregressive moving average (ARMA) model. The first purpose of this paper is to apply the autoregressive (AR), moving average (MA) or ARMA models to the observations to predict stock returns. There are four procedures which is used to build an AR, MA, or ARMA model. First, the observations must be weakly stationary. Second, the order of the models must be identified to obtain the best model. Third, the unknown parameters of the models are estimated by maximum likelihood. Fourth, through residual analysis, diagnostic checks are performed to determine the adequacy of the model. In this paper, stock returns of BCA are used as data observation. Finally, the ARMA (1,1) model is the best model and appropriate to predict the stock returns BCA in the future.

The Commutation Matrices of Elements in Kronecker Quaternion Groups Yanita Yanita; Eka Purwanti; Lyra Yulianti
Jambura Journal of Mathematics Vol 4, No 1: January 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

This article discusses the commutation matrix in the Kronecker quaternion group; that is, a non-abelian group whose 32 elements are matrices of 4 × 4 size, with entries in the set of complex numbers. The purpose of this paper is to describe the commutation matrices obtained in relation to the matrices in this group. The commutation matrix is a permutation matrix that associates the relationship between the vec and vec of the transpose matrix. Based on the classification of matrices in the Kronecker quaternion group, there are 16 classification of commutation matrices for the matrices in this group.

Penentuan Harga Opsi Dengan Volatilitas Stokastik Menggunakan Metode Monte Carlo Chalimatusadiah Chalimatusadiah; Donny Citra Lesmana; Retno Budiarti
Jambura Journal of Mathematics Vol 3, No 1: January 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

ABSTRAKHal yang utama dalam perdagangan opsi adalah penentuan harga jual opsi yang optimal. Namun pada kenyataan sebenarnya fluktuasi harga aset yang terjadi di pasar menandakan bahwa volatilitas dari harga aset tidaklah konstan, hal ini menyebabkan investor mengalami kesulitan dalam menentukan harga opsi yang optimal. Artikel ini membahas tentang penentuan harga opsi tipe Eropa yang optimal dengan volatilitas stokastik menggunakan metode Monte Carlo dan pengaruh harga saham awal, harga strike, dan waktu jatuh tempo terhadap harga opsi Eropa. Adapun model volatilitas stokastik yang digunakan dalam penelitian ini adalah model Heston, yang mengasumsikan bahwa proses harga saham (St) mengikuti distribusi log-normal, dan proses volatilitas saham (Vt) mengikuti Proses Cox-Ingersoll-Ross. Hal pertama yang dilakukan dalam penelitian ini adalah mengestimasi parameter model Heston untuk mendapatkan harga saham dengan menggunakan metode ordinary least square dan metode numerik Euler-Maruyama. Langkah kedua adalah melakukan estimasi harga saham untuk mendapatkan harga opsi tipe Eropa menggunakan metode Monte Carlo. Hasil dari penelitian ini menunjukkan bahwa penggunaan metode Monte Carlo dalam penentuan harga opsi tipe Eropa dengan volatilitas stokastik model Heston menghasilkan solusi yang cukup baik karena memiliki nilai error yang kecil dan akan konvergen ke solusi eksaknya dengan semakin banyak simulasi. Selain itu, simulasi Monte Carlo memberikan kesimpulan bahwa parameter harga strike, harga saham awal dan waktu jatuh tempo memiliki pengaruh terhadap harga opsi yang konsisten dengan teori harga opsi. ABSTRACTWhat is important in options trading is determining the optimal selling price. However, in real market conditions, fluctuations in asset prices that occur in the market indicate that the volatility of asset prices is not constant, this causes investors to experience difficulty in determining the optimal option price. This article discusses the optimal determination of the European type option price with stochastic volatility using the Monte Carlo method and the effect of the initial stock price, strike price, and expiration date on European option prices. The stochastic volatility model used in this study is the Heston model, which assumes that the stock price process (S) follows the normal log distribution, and the stock volatility process (V) follows the Ingersoll-Ross Cox Process. The first thing to do in this study is to estimate the parameters of the Heston model to get stock prices using the ordinary least square method and the Euler-Maruyama numerical method. The second step is to estimate the share price to get the European type option price using a Monte Carlo Simulation. This study indicates that using the Monte Carlo method in determining the price of European type options with the Heston model of stochastic volatility produces a fairly good solution because it has a small error value and will converge to the exact solution with more simulations. Also, the Monte Carlo simulation concludes that the parameters of the strike price, initial stock price, and maturity date influence the option price, which is consistent with the option price theory.

Stability of Traveling Waves to a Burgers Equation with 2nd-Order Nonlinear Diffusion Mohammad Ghani
Jambura Journal of Mathematics Vol 4, No 1: January 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

We are interested in the study of asymptotic stability for Burgers equation with second-order nonlinear diffusion. We first transform the original equation by the ansatz transformation to establish the existence of traveling wave. We further employ the energy estimate under small perturbation and arbitrary wave amplitude. This energy estimate is then used to establish the stability.

Pemodelan Geographically Weighted Logistic Regression dengan Fungsi Adaptive Gaussian Kernel Terhadap Kemiskinan di Provinsi NTT Novia Amilatus Solekha; Mohammad Farhan Qudratullah
Jambura Journal of Mathematics Vol 4, No 1: January 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

The Geographically Weighted Logistic Regression (GWLR) model is a logistic regression model development that is applied to spatial data from non-stationary processes. This model is used to predict a model of the data set that has a binary response variable which takes into account the spatial factor. This study will discuss the use of the GWLR model using the adaptive weighting function of the Gaussian kernel in a poverty case study in East Nusa Tenggara Province in 2019.The parameter estimation of the Maximum Likelihood Estimation (MLE) method by giving different weights for each observation location. The weight used is the adaptive Gaussian kernel with the optimum bandwidth selection using the Cross-Validation (CV). Based on the results of testing the parameters of the GWLR model with a weighted adaptive Gaussian kernel, it can be concluded that the factors that influence poverty are local and vary in the 22 observation locations, including GRDP per capita, acceptance of smart Indonesian programs, and projected population growth rates, with a classification accuracy rate of 81,82%.

fq-derivasi di BM-aljabar Egytia Yattaqi; Sri Gemawati; Ihda Hasbiyati
Jambura Journal of Mathematics Vol 3, No 2: July 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

ABSTRAK B-aljabar adalah suatu himpunan tak kosong X dengan operasi biner dan konstanta 0 yang memenuhi aksioma-aksioma tertentu. Suatu bentuk khusus dari B-aljabar adalah BM-aljabar. Adapun hubungan kedua aljabar tersebut, setiap BM-aljabar adalah B-aljabar dan setiap B-aljabar 0-komutatif adalah BM-aljabar. Konsep fq-derivasi telah dibahas di B-aljabar. Pada artikel ini, dibahas konsep fq-derivasi di BM-aljabar. Hasil penelitian yang diperoleh adalah mendefinisikan inside dan outside fq-derivasi di BM-aljabar dan menentukan sifat-sifatnya. Adapun definisi fq-derivasi di BM-aljabar ekuivalen dengan fq-derivasi di B-aljabar, namun pada sifat-sifatnya terdapat perbedaan, yaitu terdapat sifat fq-derivasi yang berlaku di BM-aljabar tetapi secara umum tidak berlaku di B-aljabar. ABSTRACTB-algebra is a non-empty set X with a constant 0 and binary operation satisfying certain axioms. A special form of B-algebra is BM-algebra. Their relationship are every BM-algebra is a B-algebra and every 0-commutative B-algebra is a BM-algebra. The concept of fq-derivation in B-algebra is discussed. The results define inside and outside fq-derivations in BM-algebra and obtain related properties. Moreover, the definition of fq-derivation in BM-algebra is equivalent to fq-derivation in B-algebra, but there are differences in their properties, which is there are some properties of fq-derivation in BM-algebra, but generally don’t hold in B-algebra.

Bilangan Terhubung Titik Pelangi pada Graf Hasil Operasi Korona Graf Prisma (P_(m,2)) dan Graf Lintasan (P_3) Indrawati Lihawa; Sumarno Ismail; Isran K Hasan; Lailany Yahya; Salmun K Nasib; Nisky Imansyah Yahya
Jambura Journal of Mathematics Vol 4, No 1: January 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Rainbow vertex-connection number is the minimum k-coloring on the vertex graph G and is denoted by rvc(G). Besides, the rainbow-vertex connection number can be applied to some special graphs, such as prism graph and path graph. Graph operation is a method used to create a new graph by combining two graphs. Therefore, this research uses corona product operation to form rainbow-vertex connection number at the graph resulting from corona product operation of prism graph and path graph (Pm,2 P3) (P3 Pm,2). The results of this study obtain that the theorem of rainbow vertex-connection number at the graph resulting from corona product operation of prism graph and path graph (Pm,2 P3) (P3 Pm,2) for 3 = m = 7 are rvc (G) = 2m rvc (G) = 2.

Simulasi Dampak Penghalang pada Gelombang Tsunami Menggunakan Persamaan Air Dangkal dengan Metode Beda Hingga Ahmad Zaenal Arifin
Jambura Journal of Mathematics Vol 3, No 2: July 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

ABSTRAKTsunami menjadi salah satu bencana alam yang paling berbahaya di daerah sekitar pesisir. Dampak dari gelombang tsunami menyebabkan kerugian yang besar bagi manusia, adanya banyak korban jiwa dan juga besarnya kerugian dalam bidang ekonomi. Artikel ini menunjukkan simulasi dengan pendekatan numerik metode beda hingga untuk menunjukkan dampak keberadan barrier sebagai penghalang gelombang tsunami. Gelombang tsunami dapat direpresntasikan dengan menggunakan persamaan air dangkal. Persamaan air dangkal secara umum digunakan dalam menggambarkan masalah fluida yang didasari oleh konservasi fisik dan juga dapat digunakan untuk menggambarkan terjadinya gelombang tsunami. Persamaan air dangkal berbentuk persamaan diferensial parsial sehingga dapat diselesaikan menggunakan metode beda hingga. Hasil simulasi persamaan air dangkal menunjukan bahwa persamaan air dangkal dapat merepresentasikan gelombang tsunami dengan konstruksi penghalang dan diketahui bahwa pembangunan sebuah penghalang dapat memecah gelombang tsunami dan dapat mengurangi kekuatan gelombang. ABSTRACTOne of the most dangerous natural disasters in the coastal area is Tsunami. The tsunami waves impact caused considerable losses to humans, many casualties, and significant losses in the economic field. This article shows a simulation using the numerical approach of finite difference methods to deliver the barrier's impact is a tsunami wave barrier. Tsunami waves can be represented using the shallow water equation. The shallow water equation is generally used to describe fluid problems based on physical conservation and define tsunami waves. The shallow water equation is in the form of a partial differential equation to be solved using the finite difference method. The shallow water equation's simulation results show that the shallow water equation can represent a tsunami wave with a barrier construction. It is known that the construction of a barrier can break the tsunami waves and reduce the strength of the waves.

Pendekatan Univariate Time Series Modelling untuk Prediksi Kuartalan Pertumbuhan Ekonomi Indonesia Pasca Vaksinasi COVID-19 Asrirawan Asrirawan; Sri Utami Permata; Muhammad Ilham Fauzan
Jambura Journal of Mathematics Vol 4, No 1: January 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

The development of COVID-19 has had a significant negative impact on Indonesia’s economic growth based on the indicator of the value of the quarterly year of year data in 2020 and 2021. Economic growth is still experiencing a recession per first quarter with a percentage of - 2.19 percent at the beginning of 2021. The government has to take vaccination measures for the community gradually with the aim of reducing the number of sufferers of these cases. The purpose of this study is to predict economic growth quarterly after vaccination using 3 (three) univariate time series models, namely ARIMA, Holt-Winters and Dynamic Linear models for policymaking. Holt-Winters and Dynamic Linear models make it possible to handle time-series data containing trends and seasonality. The data is divided into training data and test data obtained from the ministry of finance and the Indonesian Central Statistics Agency (BPS). The goodness of the model uses MSE, MAE and U-Theil criteria. Based on the results of the analysis using the R library, the results show that the best modelling for economic growth data is the ARIMA model with the lowest MSE, MAE and U-Theil values with the difference between the models being 0.000242. The ARIMA model looks better than other models because the economic growth data only contains trends and assumes a seasonal element in the data. In addition, the Holt-Winters and Dynamic Linear models produce a forecast for Indonesia’s economic growth to still experience a recession (negative growth) in the next four quarterly data, while the ARIMA model produces a positive growth forecast in the fourth quarter.

Model Petri Net Sistem Pembayaran Pajak Kendaraan Bermotor Jenis 5 Tahun Nurlela Nurlela; Ahmad Faisol; Fitriani Fitriani
Jambura Journal of Mathematics Vol 4, No 1: January 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Paying taxes is an example of public service. In the process of serving, the service is often synonymous with the queuing process. Queuing is a condition in which several people or objects from a waiting line to be served are generally caused by the need for services to exceed the service capacity or service facilities so that users of arriving facilities cannot immediately receive service. Therefore, overcoming many complaints due to queues can be done by improving services and maximizing time efficiency using the Petri net model. In this study, a Petri net model of the 5-year tax payment service system for a motor vehicle at SAMSAT Oku Timur 1 was made as many as 17 places, 15 transitions, two operators, and 30 arcs using WOPED 3.2.0 software.

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Home Page

OAI Link

Editorial Team

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Contact Name Resmawan

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Phone +6285255230451

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Editorial Address Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango, Gorontalo, Indonesia

Location Kota gorontalo, Gorontalo INDONESIA

Abstract

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Abstract

Contact Name
Resmawan

Contact Email
resmawan@ung.ac.id

Phone
+6285255230451

Journal Mail Official
info.jjom@ung.ac.d

Editorial Address
Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango, Gorontalo, Indonesia

Location
Kota gorontalo,

Gorontalo

INDONESIA