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Jambura Journal of Mathematics
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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Search results for , issue "Vol 3, No 1: January 2021" : 7 Documents clear
Effect of Prey Refuge and Harvesting on Dynamics of Eco-epidemiological Model with Holling Type III Adin Lazuardy Firdiansyah
Jambura Journal of Mathematics Vol 3, No 1: January 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (520.92 KB) | DOI: 10.34312/jjom.v3i1.7281

Abstract

In this research, we formulate and analyze an eco-epidemiology model of the modified Leslie-Gower model with Holling type III by incorporating prey refuge and harvesting. In the model, we find at most six equilibrium where three equilibrium points are unstable and three equilibrium points are locally asymptotically stable. Furthermore, we find an interesting phenomenon, namely our model undergoes Hopf bifurcation at the interior equilibrium point by selecting refuge as the bifurcation parameter. Moreover, we also conclude that the stability of all populations occurs faster when the harvesting rate increases.  In the end, several numerical solutions are presented to check the analytical results.
Peramalan Nilai Tukar Petani Subsektor Peternakan Menggunakan Fuzzy Time Series Lee Mahadi Muhammad; Sri Wahyuningsih; Meiliyani Siringoringo
Jambura Journal of Mathematics Vol 3, No 1: January 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (648.747 KB) | DOI: 10.34312/jjom.v3i1.5940

Abstract

ABSTRAKFuzzy time series (FTS) Lee adalah suatu metode peramalan yang digunakan ketika jumlah data historis yang tersedia sedikit, serta tidak mensyaratkan asumsi-asumsi tertentu yang harus terpenuhi. Metode ini menggunakan data historis berupa himpunan fuzzy yang berasal dari bilangan real atas himpunan semesta pada data aktual. FTS Lee adalah perkembangan dari FTS Song dan Chissom, FTS Cheng, serta FTS Chen. Pada penelitian ini dibahas penerapan FTS Lee pada data Nilai Tukar Petani Subsektor Peternakan (NTPT) di Kalimantan Timur. Tujuan penelitian ini adalah memperoleh hasil peramalan NTPT di Kalimantan Timur pada bulan Januari 2020 dengan menggunakan FTS Lee. Langkah awal dalam penelitian ini yaitu menentukan himpunan semesta pembicaraan, langkah kedua menentukan banyaknya himpunan fuzzy, langkah ketiga mendefinisikan derajat keanggotaan himpunan fuzzy terhadap  dan melakukan fuzzyfikasi pada data aktual, langkah keempat membuat fuzzy logical relationship, langkah kelima membuat fuzzy logical relationship group, langkah keenam melakukan defuzzyfikasi sehingga diperoleh hasil peramalan, serta dilanjutkan dengan menghitung nilai mean absolute percentage error. Hasil penelitian menunjukkan bahwa peramalan menggunakan FTS Lee pada bulan Januari 2020 adalah 110,25. Nilai mean absolute percentage error pada  hasil peramalan dengan menggunakan FTS Lee adalah sangat baik.  ABSTRACTLee’s Fuzzy time series (FTS) is a forecasting method that is used when the number of historical data that available was small and does not require certain assumptions to be fulfilled. This method uses historical data in the form of fuzzy sets derived from real numbers over the set of universes in the actual data. FTS Lee is a development of FTS Song and Chissom, FTS Cheng, and FTS Chen. This research discusses the application of FTS Lee to the Exchange Rate of Farmers Subsectors Farm (ERFSF) in Kalimantan Timur. The purpose of this study was to obtain the results of ERFSF forecasting in Kalimantan Timur in January 2020 using FTS Lee. The first step during research is to determine the set of speech universes, the second step is to determine the number of fuzzy sets, the third step is to define the degree of fuzzy association membership and fuzzification on the actual data, the fourth step is to create a fuzzy logical relationship, the fifth step is to create a fuzzy logical relationship group, the sixth step is to perform defuzzification in order to obtain forecasting results, and continue by calculating the mean absolute percentage error value. The results showed that forecasting using FTS Lee in January 2020 was 110,25. The mean absolute percentage error value in forecasting results using FTS Lee is very good.
Analisis Dinamik Model Transmisi COVID-19 dengan Melibatkan Intervensi Karantina Resmawan Resmawan; Agusyarif Rezka Nuha; Lailany Yahya
Jambura Journal of Mathematics Vol 3, No 1: January 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (609.878 KB) | DOI: 10.34312/jjom.v3i1.8699

Abstract

ABSTRAKMakalah ini membahas dinamika transmisi COVID-19 dengan melibatkan intervensi karantina. Model dikonstruksi dengan melibatkan tiga kelas penyebab infeksi, yaitu kelas manusia terpapar, kelas manusia terinfeksi tanpa gejala klinis, dan kelas manusia terinfeksi disertai gejala klinis. Variabel yang merepresentasikan intervensi karantina untuk menekan pertumbuhan infeksi juga dipertimbangkan pada model. Selanjutnya, analisis model difokuskan pada eksistensi titik kesetimbangan dan simulasi numerik untuk menunjukkan dinamika populasi secara visual. Model yang dikonstruksi membentuk model SEAQIR yang memiliki dua titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik. Analisis kestabilan menunjukkan bahwa titik kesetimbangan bebas penyakit bersifat stabil asimtotik lokal pada saat R01 dan tidak stabil pada saat R01. Simulasi numerik menunjukkan bahwa peningkatan intervensi berupa karantina dapat berkontribusi memperlambat transmisi COVID-19 sehingga diharapkan dapat mencegah terjadinya wabah pada populasi.ABSTRACTThis paper discusses the dynamics of COVID-19 transmission by involving quarantine interventions. The model was constructed by involving three classes of infectious causes, namely the exposed human class, asymptotically infected human class, and symptomatic infected human class. Variables were representing quarantine interventions to suppress infection growth were also considered in the model. Furthermore, model analysis is focused on the existence of equilibrium points and numerical simulations to visually showed population dynamics. The constructed model forms the SEAQIR model which has two equilibrium points, namely a disease-free equilibrium point and an endemic equilibrium point. The stability analysis showed that the disease-free equilibrium point was locally asymptotically stable at R01 and unstable at R01. Numerical simulations showed that increasing interventions in the form of quarantine could contribute to slowing the transmission of COVID-19 so that it is hoped that it can prevent outbreaks in the population.
Peramalan Harga Emas Saat Pandemi Covid-19 Menggunakan Model Hybrid Autoregressive Integrated Moving Average - Support Vector Regression Drajat Indra Purnama
Jambura Journal of Mathematics Vol 3, No 1: January 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (393.603 KB) | DOI: 10.34312/jjom.v3i1.8430

Abstract

ABSTRAKInvestasi emas merupakan salah satu investasi yang menjadi favorit dimasa pandemi Covid 19 seperti sekarang ini. Hal ini dikarenakan harga emas yang nilainya relatif fluktuatif tetapi menunjukkan tren peningkatan. Investor dituntut pandai dalam berinvestasi emas, mampu memprediksi peluang dimasa yang akan datang. Salah satu model peramalan data deret waktu adalah model Autoregressive Integrated Moving Average (ARIMA). Model ARIMA baik digunakan pada data yang berpola linear tetapi jika digunakan pada data data nonlinear keakuratannya menurun. Untuk mengatasi permasalahan data nonlinear dapat menggunakan model Support Vector Regression (SVR). Pengujian linearitas pada data harga emas menunjukkan adanya pola data linear dan nonlinear sekaligus sehingga digunakan kombinasi ARIMA dan SVR yaitu model hybrid ARIMA-SVR. Hasil peramalan menggunakan model hybrid ARIMA-SVR menunjukkan hasil lebih baik dibanding model ARIMA. Hal ini dibuktikan dengan nilai MAPE model hybrid ARIMA-SVR lebih kecil dibandingkan nilai MAPE model ARIMA. Nilai MAPE model hybrid ARIMA-SVR sebesar 0,355 pada data training dan 4,001 pada data testing, sedangkan nilai MAPE model ARIMA sebesar 0,903 pada data training dan 4,076 pada data testing.ABSTRACTGold investment is one of the favorite investments during the Covid 19 pandemic as it is today. This is because the price of gold is relatively volatile but shows an increasing trend. Investors are required to be smart in investing in gold, able to predict future opportunities. One of the time series data forecasting models is the Autoregressive Integrated Moving Average (ARIMA) model. The ARIMA model is good for use on linear patterned data but if it is used on nonlinear data the accuracy decreases. To solve the problem of nonlinear data, you can use the Support Vector Regression (SVR) model. The linearity test on the gold price data shows that there are linear and nonlinear data patterns at the same time so that a combination of ARIMA and SVR is used, namely the ARIMA-SVR hybrid model. Forecasting results using the ARIMA-SVR hybrid model show better results than the ARIMA model. This is evidenced by the MAPE value of the ARIMA-SVR hybrid model which is smaller than the MAPE value of the ARIMA model. The MAPE value of the ARIMA-SVR hybrid model is 0.355 on the training data and 4.001 on the testing data, while the MAPE value of the ARIMA model is 0.903 in the training data and 4.076 in the testing data.
Peramalan Gelombang Covid 19 Menggunakan Hybrid Nonlinear Regression Logistic – Double Exponential Smoothing di Indonesia dan Prancis I Gusti Bagus Ngurah Diksa
Jambura Journal of Mathematics Vol 3, No 1: January 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (624.967 KB) | DOI: 10.34312/jjom.v3i1.7771

Abstract

ABSTRAKIndonesia dan Prancis adalah dua Negara yang mengalami Covid 19 dengan pola pergerakan kasus Covid 19 yang berbeda. Kondisi Indonesia masih mengalami siklus one wave namun Prancis sudah masuk pada pola second wave. Makna second wave adalah kondisi epidemi Covid 19 yang baru muncul setelah epidemi sebelumnya dianggap selesai. Dalam peramalan kasus Covid 19 baik itu terkait informasi puncak dari terjadinya kasus Covid 19 serta ramalan terkait akan berakhirnya pandemi kasus Covid 19 suatu negara merupakan hal penting bagi pemerintah suatu Negara. Model hybrid meningkatkan akurasi ramalan dibandingkan model time series yang dilakukan secara terpisah. Tujuan penelitian ini adalah melakukan peramalan kasus Covid 19 di Indonesia dan Prancis dengan menggunakan metode hybrid dan membandingkan dengan peramalan dengan salah satu metode tunggal. Metode yang digunakan adalah metode tunggal yaitu Nonlinear Regression Logistic dan metode Hybrid Nonlinear Regression Logistic–Double Eksponensial Smoothing. Hasilnya adalah model peramalan Hybrid Nonlinear Regression Logistic and Doubel Exponential Smoothing lebih bagus digunakan dalam peramalan kasus Covid 19 di Indonesia dan Prancis. Terlihat bahwa nilai MAPE model Hybrid Nonlinear Regression Logistic–Double Eksponensial Smoothing jauh lebih kecil dibandingkan model peramalan Nonlinear Regression Logistic. ABSTRACTIndonesia and France are two countries that have experienced Covid 19 with different patterns of movement of Covid 19 cases. Indonesia's condition is still experiencing a one wave cycle but France has entered into the second wave pattern. The meaning of the second wave is the condition of the Covid 19 epidemic which only emerged after the previous epidemic was considered over. In forecasting the Covid 19 case, whether it is related to the peak information on the occurrence of the Covid 19 case and predictions regarding the end of the pandemic of the Covid 19 case in a country, it is important for the government of a country. The hybrid model improves forecast accuracy compared to the time series model which is carried out separately. The purpose of this study is to forecast the cases of Covid 19 in Indonesia and France using the hybrid method and comparing with forecasting with one single method. The method used is a single method, namely Nonlinear Logistic Regression and Hybrid Nonlinear Regression Logistic-Double Exponential Smoothing methods. The result is that the Hybrid Nonlinear Regression Logistic and Double Exponential Smoothing forecasting model is better used in forecasting the Covid 19 cases in Indonesia and France. It can be seen that the MAPE value of the Hybrid Nonlinear Regression Logistic – Double Exponential Smoothing model is much smaller than the Nonlinear Regression Logistic forecasting model.
Pemodelan Regresi Nonparametrik dengan Estimator Spline Truncated vs Deret Fourier Andrea Tri Rian Dani; Narita Yuri Adrianingsih
Jambura Journal of Mathematics Vol 3, No 1: January 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (484.641 KB) | DOI: 10.34312/jjom.v3i1.7713

Abstract

ABSTRAKPendekatan regresi nonparametrik digunakan apabila hubungan antara variabel prediktor dan variabel respon tidak diketahui polanya. Spline truncated dan deret Fourier merupakan estimator dalam pendekatan nonparametrik yang terkenal, karena memiliki fleksibilitas yang tinggi dan mampu menyesuaikan terhadap sifat lokal data secara efektif. Penelitian ini bertujuan untuk mendapatkan estimator model regresi nonparametrik terbaik menggunakan spline truncated dan deret Fourier. Metode estimasi kurva regresi nonparametrik dilakukan dengan menyelesaikan optimasi Ordinary Least Squares (OLS). Kriteria kebaikan model menggunakan GCV, R2 dan MSE. Pemodelan regresi nonparametrik diterapkan pada data Case Fatality Rate (CFR) akibat Demam Berdarah Dengue (DBD) di Indonesia.  Berdasarkan hasil analisis, hasil estimasi dari pemodelan regresi nonparametrik menunjukkan bahwa estimator spline truncated memberikan performa yang lebih baik dibandingkan estimator deret Fourier. Hal ini ditunjukkan dengan nilai R2 dari estimator spline truncated yaitu sebesar 91,80% dan MSE sebesar 0,04, sedangkan dengan estimator deret Fourier diperoleh nilai R2 sebesar 65,44% dan MSE sebesar 0,19.ABSTRACTThe nonparametric regression approach is used when the relationship between the predictor variable and the response variable is unknown. Spline truncated and Fourier series are well-known estimators in the nonparametric approach because they have high flexibility and are able to adjust to the local properties of the data effectively. This study aims to obtain the best nonparametric regression model estimator using the truncated spline and the Fourier series. The nonparametric regression curve estimation method is done by completing the Ordinary Least Squares (OLS) optimization. The criteria for the goodness of the model use GCV, R2, and MSE. Nonparametric regression modeling is applied to Case Fatality Rate (CFR) modeling due to Dengue Hemorrhagic Fever (DBD) in Indonesia. Based on the analysis, the estimation results from the nonparametric regression modeling show that the truncated spline estimator provides better performance than the Fourier series estimator. This is shown by the R2 value of the truncated spline estimator which is 91.80% and the MSE is 0.04, while the Fourier series estimator obtained an R2 value of 65.44% and MSE of 0.19.
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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (430.844 KB) | DOI: 10.34312/jjom.v3i1.10137

Abstract

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.

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