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Jurnal Matematika UNAND
Published by Universitas Andalas
ISSN : 2303291X     EISSN : 27219410     DOI : -
Core Subject : Science, Education,
Computer Science & IT Mathematics
Fokus dan Lingkup dari Jurnal Matematika FMIPA Unand meliputi topik-topik dalam Matematika sebagai berikut : Analisis dan Geometri Aljabar Matematika Terapan Matematika Kombinatorika Statistika dan Teori Peluang.
Arjuna Subject : -
Articles 858 Documents
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MODEL CAPITAL ASSET PRICING MODEL (CAPM) DALAM PEMBENTUKAN PORTOFOLIO OPTIMAL SAHAM JAKARTA ISLAMIC INDEX (JII) NOVALISA NASTHASYA; Hazmira Yozza; DODI DEVIANTO
Jurnal Matematika UNAND Vol 12, No 4 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.4.299-308.2023

Abstract

Dalam berinvestasi saham, setiap investor ingin mendapatkan return yang tinggi dan risiko yang rendah. Salah satu cara untuk meminimalisir risiko adalah dengan membentuk portofolio optimal yang menguntungkan dari segi return dan risiko. Pada penelitian ini digunakan Capital Asset Pricing Model (CAPM) dalam membentuk portofolio optimal. Data yang digunakan adalah data saham dalam Jakarta Islamic Index (JII) periode Desember 2020-November 2021. Pemodelan menghasilkan 5 saham penyusun komposisi portofolio optimal. Return eskpektasi portofolio sebesar 0,015282 dan risiko portofolio sebesar 0,069750. Evaluasi kinerja portofolio optimal yang terbentuk diukur berdasarkan ukuran rasio Sharpe, Modigliani Square dan Treynor. Dari hasil penelitian didapat bahwa portofolio optimal yang dibentuk dengan Capital Asset Pricing Model (CAPM) layak untuk diinvestasikan.
ANALISIS KESTABILAN MODEL MATEMATIKA AKSI DEMONSTRASI MAHASISWA DI SUMATERA BARAT Yolanda Putri; ARRIVAL RINCE PUTRI; RIRI LESTARI
Jurnal Matematika UNAND Vol 12, No 3 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.3.213-221.2023

Abstract

Aksi demonstrasi atau unjuk rasa merupakan salah satu fenomena di dunia nyata yang sering terjadi dan melibatkan berbagai kalangan, baik mahasiswa, buruh, maupun anggota suatu organisasi. Khususnya di Sumatera Barat, pada tanggal 23 dan 25 September 2019 telah terjadi demonstrasi polemik RUU di gedung DPRD Sumatera Barat yang melibatkan ribuan mahasiswa, aparat kepolisian, dan anggota DPRD Tingkat I.Pada penelitian ini dibahas model matematika aksi demonstrasi mahasiswa. Model ini merujuk pada model Richardson. Model dianalisis kestabilannya melalui analisis kestabilan titik ekuilibrium. Kestabilan titik ekuilibrium ditentukan dari nilai eigen matriks koefisien yang diperoleh. Hasil analitik dikonfirmasi dengan hasil numerik. Parameter model yang digunakan pada simulasi numerik diperoleh dari data yang diolah berdasarkan kuisioner yang diambil dari responden. Berdasarkan hasil yang diperoleh dapat disimpulkan bahwa aksi demonstrasi yang terjadi berlangsung anarkis. Hal ini sesuai dengan kenyataan yang terjadi di lapangan bahwa aksi demonstrasi yang terjadi pada kasus demonstrasi polemik RUU di gedung DPRD Sumatera Barat tanggal 25 September 2019 merupakan demonstrasi anarkis. 
PERFORMA KLASIFIKASI DATA TIDAK SEIMBANG DENGAN PENDEKATAN MACHINE LEARNING (STUDI KASUS: DIABETES INDIAN PIMA) Masjidil Aqsha; Nurtiti Sunusi
Jurnal Matematika UNAND Vol 12, No 2 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.2.176-193.2023

Abstract

Diabetes merupakan suatu penyakit atau gangguan metabolisme kronis dengan multi etiologi yang ditandai dengan tingginya kadar gula darah disertai dengan gangguan metabolisme karbohidrat, lipid, dan protein sebagai akibat insufisiensi fungsi insulin. Faktor risiko diabetes berhubungan dengan status diabetes sesorang. Berbagai pendekatan machine learning menjadi alternatif dalam memprediksi status diabetes. Namun, dalam banyak kasus, data yang tersedia tidak cukup seimbang dalam kelas datanya. Adanya ketidakseimbangan data dapat menyebabkan hasil prediksi menjadi tidak akurat. Tujuan penelitian dalam paper ini adalah untuk mengatasi masalah ketidakseimbangan data dan membandingkan kinerja model dalam memprediksi status diabetes. Secara umum, metode seperti Synthetic Minority Over-sampling Technique (SMOTE) dan Adaptive Synthetic (ADASYN) dapat digunakan untuk menyeimbangkan data. Data Diabetes Indian Pima yang telah diseimbangkan kemudian diprediksi dengan metode machine learning seperti metode Bagging, Random Forest, dan XGBoost. Hasil penelitian menunjukkan bahwa performa model machine learning meningkat setelah menangani ketidakseimbangan data dan model terbaik adalah model XGBoost. 
ANALISIS PERPINDAHAN PENGGUNAAN APLIKASI TRANSPORTASI ONLINE MENGGUNAKAN RANTAI MARKOV Salmun K. Nasib; Nurwan Nurwan; I Wayan Can Aryasandi; Isran K. Hasan; Asriadi Asriadi
Jurnal Matematika UNAND Vol 13, No 1 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.1.26-40.2024

Abstract

The purpose of this study is to find out the opportunities for switching to the use of online transportation applications and predict the future use of online transportation applications by Gorontalo State University students using the Markov chain. The data used in this study are primary data obtained through questionnaires. The results of the prediction of the proportion for future market share show that the proportion of users of the Maxim transportation application is 82.89%, Grab is 7.75%, Gojek is 5.06% and InDriver is 4.48%.
AN AREA OF RIGHT TRIANGLE FOR TRIGONOMETRY MOCHAMMAD IDRIS; MOHAMMAD MAHFUZH SHIDDIQ; ERIDANI ERIDANI
Jurnal Matematika UNAND Vol 12, No 4 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.4.267-275.2023

Abstract

In this paper, we shall investigate formula of tangent function through determination of area of right triangle and rectangle. The consequence of this formula is used to obtain the other two trigonometric function, i.e. sine and cosine functions. Moreover, we also reprove Pythagorean theorem.
KESTABILAN LOKAL TITIK EKUILIBRIUM MODEL PENYEBARAN PENYAKIT POLIO Joko Harianto; Venthy Angelika; Feby Seru
Jurnal Matematika UNAND Vol 12, No 2 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.2.153-167.2023

Abstract

The fact shows that polio is very dangerous to humanity, it is necessary to study the dynamics of the spread of polio. One way, namely a mathematical approach in the form of a mathematical model for the spread of polio. The mathematical model used in this study is the SEIV model. This study aims to provide a description of the dynamics of the spread of polio. The results of this study are expected to be used as a reference to study the dynamics of the spread of polio in an area. The method used in the implementation of this research is literature study. The first stage starts with the model formulation. The second stage analyzes the model that has been formed and the last one makes a model simulation. The formed SEIV model is a system of nonlinear differential equations. The basic reproduction number  parameter is obtained from the analysis of the system. If the basic reproduction number less than one, then there is a single point of  free disease equilibrium that is locally stable asymptotically. Conversely, if the basic reproduction number more than one, then there are two points of equilibrium, namely the point of free equilibrium of disease  and the endemic equilibrium point . When the basic reproduction number more than one endemic equilibrium point  is stable asymptotically locally. Based on the simulation, if  the basic reproduction number less than one for t → ∞ and value (S, E, I, V) are close enough to E*, the system solution will move to E*. This means that if the basic reproduction number less than one, the disease will not be endemic and tends to disappear in an infinite amount of time. Conversely, if the basic reproduction number more than one for t → ∞ and the value (S, E, I, V) are close enough to E^, then the system solution will move towards E^. This means that if the basic reproduction number more than one, then the disease will remain in the population but not reach extinction in an infinite amount of time
ARIMA-GARCH MODEL IN OVERCOMING HETEROSCHEDSDATICITY IN STOCK PRICE PREDICTION (CASE STUDY: PT INDOFOOD, TBK (INDF)) MUHAMMAD RIZAL; ALBERTUS EKA PUTRA HARYANTO; NI KADEK JULIARINI
Jurnal Matematika UNAND Vol 13, No 2 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.2.91-105.2024

Abstract

Ensuring access to future stock price information holds significant weight for investors in formulating investment strategies. The Indonesian capital market serves pivotal economic and financial roles within the economy, offering various instruments, such as stocks. Among these, blue-chip stocks are recognized for their minimal risk exposure. The impact of the COVID-19 pandemic is anticipated to influence stock price dynamics, including those of blue-chip stocks. Statistical methodologies, such as Autoregressive Integrated Moving Average (ARIMA), are commonly utilized for stock price prediction. However, the efficacy of ARIMA is contingent upon the fulfillment of homoscedasticity assumptions. Failure to meet this assumption due to fluctuating stock price developments poses a challenge. Consequently, an ARIMA-GARCH hybrid model has been developed to address heteroskedasticity concerns in stock price forecasting. This study focuses on INDF stock data, exemplifying a blue-chip stock with positive performance. Results indicate that combining ARIMA-GARCH models, particularly the ARIMA(0,1,3)-GARCH(1,3) model, yields optimal predictions for subsequent stock prices. The MAPE value of the ARIMA-GARCH model stands at 1.41%, indicating superior performance compared to standalone ARIMA modeling. These findings are expected to serve as a valuable resource for investors navigating investment decisions. 
BILANGAN RAMSEY MULTIPARTIT HIMPUNAN (R-M-H) M_j(C_n, C_s) UNTUK CYCLE Abdul - Majid; SYAFRIZAL SY; ADMI NAZRA
Jurnal Matematika UNAND Vol 12, No 4 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.4.309-317.2023

Abstract

Diberikan dua graf G dan H sembarang. Bilangan Ramsey multipartit himpunan (R-M-H) M_j(G, H) dengan bilangan asli j ≥ 2, adalah bilangan bulat positif terkecil t sedemikian sehingga jika semua sisi dari graf multipartit seimbang lengkap K_{t×j} diberi sebarang 2−pewarnaan merah-biru, maka graf K_{t×j} senantiasa memuat G berwarna merah sebagai subgraf atau H berwarna biru sebagai subgraf. Graf C_n adalah suatu graf cycle dengan n ≥ 3 titik. Pada artikel ini, Penulis akan menentukan bilangan R-M-H M_j(C_n, C_s) untuk sebarang bilangan asli n ≥ 3 ganjil dan s ≥ 3. Hasil dari penelitian ini adalah ditemukannya bilangan R-M-H Mj (C_n, C_s) untuk cycle.
Bilangan Kromatik Lokasi Graf Helm Hm Dengan 3 ≤ m ≤ 9 Kelson Novrianus Lessya; Des Welyyanti; Lyra Yulianti
Jurnal Matematika UNAND Vol 12, No 3 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.3.222-228.2023

Abstract

Misalkan G = (V, E) adalah graf terhubung dan c suatu k−pewarnaan dari G. Kelas warna pada G adalah himpunan titik-titik yang berwarna i, dinotasikan dengan Si untuk 1 ≤ i ≤ k. Misalkan Π = {S1, S2. · · · , Sk} merupakan partisi terurut dari V (G) kedalam kelas-kelas warna yang saling bebas. Berdasarkan pewarnaan titik, maka representasi titik v terhadap Π disebut kode warna dari v, dinotasikan dengan cΠ(v) dari suatu titik v ∈ V (G) didefinisikan sebagai k−pasang terurut, yaitu: cΠ(v) = (d(v, S1), d(v, S2), · · · , d(v, Sk)) dengan d(v, Si) = min{d(v, x)|x ∈ Si} untuk 1 ≤ i ≤ k. Jika setiap titik pada G memiliki kode warna yang berbeda terhadap Π, maka c disebut pewarnaan lokasi. Banyaknya warna minimum yang digunakan disebut bilangan kromatik lokasi, dinotasikan dengan χL(G). Pada tulisan ini akan dibahas bilangan kromatik lokasi graf helm Hm dengan 3 ≤ m ≤ 9.
GREY MARKOV (1,1) MODEL FOR FORECASTING THE PERCENTAGE OF THE POPULATION THAT EXPERIENCED HEALTH COMPLAINTS IN INDONESIA Nur'ainul Miftahul Huda; Nurfitri Imro'ah
Jurnal Matematika UNAND Vol 12, No 2 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.2.108-120.2023

Abstract

In mathematics, in addition to the time series model, Autoregressive, Moving Average, or Autoregressive Moving Average, the Grey-Markov (1,1) model can be employed for forecasting. One of the gains of this model is that it may cover a minimum quantity of data, which is beneficial in situations when the amount of data that is available is restricted but is not excessively vast. This model works well with data that does not exhibit a great deal of variability. The Grey model was further developed into the Grey-Markov model by including the idea of a Markov chain into the original model. In this particular investigation, the processes consist of first forming a sequence using a 1-Accumulated Generating Operation (1-AGO), then forming a sequence using an MGO, and finally predicting using an AGO. The procedure that came before it is actually a modeling procedure for the Grey model. In addition, in order to model Grey- Markov(1,1), it is necessary to initially compute the relative inaccuracy of the forecast that came before it. The following step is to partition the outcome of the relative error into numerous states, one for each interval of the relative error. After that, each error is categorized based on a state that has been specified in advance. The state that is defined within the class is used as the basis for making predictions. The percentage of the population in Indonesia that reports having health difficulties on a yearly basis was chosen as the case study for this research because it is relevant to the topic at hand. The data came from the Central Statistics Agency in the United Kingdom. The period covered by the data is from 1996 to 2021. The purpose of this research is to investigate the structure of the Grey-Markov Model (1,1) and provide a forecast regarding the proportion of the general population that will be affected by health issues in the year 2022. According to the findings of this research project, the forecast of the proportion of the population in Indonesia that suffered health complaints in 2022 produced predictive data that was 30.36%, with a very good accuracy value of 2.43%.

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