Eigen Mathematics Journal
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Natural Cubic Spline Method as a Method in Constructing a Life Table in Gegelang Village West Lombok
Get PDFThis research aims to reconstruct a life table based on real data obtained in Gegelang Village, West Lombok. The data used in this research is the population in 2016, the death rate in 2014-2018 and the birth rate in 2014-2018. The first step taken was to compile a rough life table using the partial data situation and full data situation methods. Both methods are included in the maximum likelihood method. After carrying out calculations, different life expectancy figures are obtained. The respective calculation results were 62.21 years for the partial data situation method and 73.07 years for the full data situation method. Next, a graduation is carried out using the natural cubic spline method on the life table obtained from a rough life table model calculation. The graphic model produced by the rough life table is fluctuating so it is necessary to graduate using the natural cubic spline method to obtain a monotonically decreasing graph. The life table model chosen for graduation is a life table whose life expectancy is close to the life expectancy of West Lombok Regency in 2015, namely 65.1 years. After graduation, the new life expectancy was found to be 66.92 years
Stock Portfolio Optimization Using Single Index Model (SIM) with Exponentially Weighted Moving Average (EWMA) Approach
Get PDFThe optimal portfolio is a combination of various assets with the aim of reducing investment risk through diversification. This study aims to conduct stock selection using K-Means Clustering and the formation of an optimal stock portfolio from the application of Single Index Model the amount of investment risk in the portfolio using the Exponentially Weighted Moving Average approach, and the amount of portfolio performance. The analysis results show that there are 5 portfolios formed. The best portfolio that can be chosen by investors depends on the investor's risk tolerance. Investors with low risk tolerance can choose Portfolio 3 consisting of ICBP and MIKA stocks with an expected return of 0.01343 and a risk of 0.00714 and a VaR of IDR 2,633,286.63. Investors with moderate risk tolerance can choose Portfolio 1 which consists of ICBP, MIKA, ACES, INCO, ITMG, MAPI, TPIA, AKRA, and MDKA stocks with an expected return of 0.022047, risk of 0.01277 and VaR of IDR 3,083,287.87. Investors with high risk tolerance can choose Portfolio 2 which consists of MIKA, TPIA, and MDKA stocks with an expected return of 0.02504 and a risk of 0.01471 and a VaR of IDR 3,553,167.10
The Decision on Selecting the Best Laptop Using Analytical Hierarchy Process and Simple Additive Weighting Method at the Faculty of MIPA University of Mataram
Get PDFLaptops have the potential to increase educational productivity in Indonesia. For example, students at the Faculty of Mathematics and Natural Sciences (MIPA) at the University of Mataram now feel involved. However, the decision to choose the right laptop according to the needs of students is difficult. The research population used was active students from the class of 2020-2023, Faculty of Mathematics and Natural Sciences (MIPA), University of Mataram. This research aims to determine the best laptop selection based on alternative laptop brands, namely Asus Vivobook, Acer 3, HP 14S, Dell Vostro 14, and Lenovo IP1. Further criteria include price, processor, Random Access Memory (RAM), Read Only Memory (ROM), and screen size. The methods used are the Analytical Hierarchy Process (AHP) and Simple Additive Weighting (SAW) methods. The research results show that the first priority position is filled by the Asus Vivobook with a weight of 0,26 for the AHP method and the Lenovo IP1 with a weight of 0,898 for the SAW method. The results of priority comparisons using euclidean distance, it was found that the most optimal method for deciding on the best laptop was the AHP method. The AHP method has a value closest to 0 (zero), namely with an average value of 0,127, while the SAW method has an average value of 0,798
Forecasting the Volatility of Tuna Fish Prices in North Sumatra using the ARCH Method in the Period January - April 2024
Get PDFTuna (Euthynnus affinis) is one of the most important fisheries commodities in Indonesia with significant economic value, especially in its contribution to fisheries export revenue. However, the price of tuna experiences significant fluctuations that can affect local and national economic stability. This study analyzes the daily price fluctuations of tuna in the North Sumatra market from January 1, 2024 to April 29, 2024 using a time series analysis approach. Daily price data were collected and analyzed to identify existing price patterns and volatility. The Autoregressive Conditional Heteroskedasticity (ARCH) model was selected to address the heteroscedasticity in the data, which suggests that the volatility of tuna prices can be well predicted based on past price behavior. The analysis steps include identifying the optimal ARCH model using the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF), as well as testing parameter significance and normality assumptions to validate the model fit. The results show that the ARMA (1,0,0) model is the optimal one to model the price volatility of yellow tuna with the MAPE obtained of 2.382. compared to the ARMA-ARCH method with the MAPE value obtained of 2,747. Because it still contains heteroskedasticity effects, even though the results are good, the prediction results do not closely match the original data. The model is effective in improving price forecasting accuracy, which is important to support decision-making in risk management and economic planning in the fisheries sector. The findings contribute to understanding the dynamics of the yellowtail market and optimizing strategies for fisheries management.Tuna (Euthynnus affinis) is one of the most important fisheries commodities in Indonesia with significant economic value, especially in its contribution to fisheries export revenue. However, the price of tuna experiences significant fluctuations that can affect local and national economic stability. This study analyzes the daily price fluctuations of tuna in the North Sumatra market from January 1, 2024 to April 29, 2024 using a time series analysis approach. Daily price data were collected and analyzed to identify existing price patterns and volatility. The Autoregressive Conditional Heteroskedasticity (ARCH) model was selected to address the heteroscedasticity in the data, which suggests that the volatility of tuna prices can be well predicted based on past price behavior. The analysis steps include identifying the optimal ARCH model using the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF), as well as testing parameter significance and normality assumptions to validate the model fit. The results show that the ARMA (1,0,0) model is the optimal one to model the price volatility of yellow tuna with the MAPE obtained of 2.382. compared to the ARMA-ARCH method with the MAPE value obtained of 2,747. Because it still contains heteroskedasticity effects, even though the results are good, the prediction results do not closely match the original data. The model is effective in improving price forecasting accuracy, which is important to support decision-making in risk management and economic planning in the fisheries sector. The findings contribute to understanding the dynamics of the yellowtail market and optimizing strategies for fisheries management
The ARIMA-GARCH Method in Case Study Forecasting the Daily Stock Price Index of PT. Jasa Marga (Persero)
Get PDFPT Jasa Marga is a large company in Indonesia that develop and operation the toll roads and is known as one of the blue chip companies with LQ45 shares. However, share prices have high volatility or rise and fall quickly so their value is always changing. Therefore, forecasting is needed to predict the share price of PT Jasa Marga in the future in order to know the movement of its share price. The Autoregressive Integrated Moving Average (ARIMA) method is a method that can predict data with high volatility, but has the disadvantage of residuals containing heteroscedasticity. So, the addition of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model was carried out to overcome the heteroscedasticity problem that was initially caused by the ARIMA model so it could predict data with high volatility more optimally. Therefore, this research applies the ARIMA-GARCH method to find the best model for forecasting the daily share price index of PT Jasa Marga. The data used comes from the daily closing stock price index of PT Jasa Marga (Persero) for the period January 2015 to May 2023. The measurement of forecasting accuracy uses the Mean Absolute Percentage Error (MAPE). The forecasting results show that the best model uses ARIMA (2,1,1) - GARCH (1,3) with a MAPE value of 6.825728%, which indicates very good forecasting results because the MAPE value is <10%.PT Jasa Marga merupakan perusahaan besar di Indonesia yang berperan dalam pengembangan dan pengoperasian jalan tol yang dikenal sebagai salah satu perusahaan blue chip dengan saham LQ45. Namun, harga sahamnya memiliki volatilitas tinggi atau naik dan turun dengan cepat sehingga nilainya selalu berubah-ubah. Oleh karena itu, diperlukan adanya peramalan guna memprediksi harga saham PT Jasa Marga di masa yang akan datang guna mengetahui pergerakan harga sahamnya. Metode Autoregressive Integrated Moving Average (ARIMA) merupakan salah satu metode yang dapat meramalkan data dengan volatilitas tinggi, namun memiliki kekurangan pada residual yang mengandung heteroskedastisitas. Sehingga, dilakukan penambahan model Generalized Autoregressive Conditional Heteroskedasticity (GARCH) guna mengatasi masalah heteroskedastisitas yang awalnya, ditimbulkan model ARIMA sehingga dapat meramalkan data dengan volatilitas tinggi secara lebih optimal. Oleh karena itu, penelitian ini menerapkan metode ARIMA-GARCH guna menemukan model terbaik untuk meramalkan indeks harga saham harian PT Jasa Marga. Data yang digunakan berasal dari indeks penutupan harga saham harian PT Jasa Marga (Persero) periode Januari 2015 hingga Mei 2023. Pengukuran ketepatan peramalan menggunakan Mean Absolute Percentage Error (MAPE). Hasil peramalan menunjukkan model terbaik menggunakan ARIMA (2,1,1) - GARCH (1,3) dengan nilai MAPE sebesar 6,825728% yang mengindikasikan hasil peramalan sangat baik karena nilai MAPE < 10%
Analisis Dinamik Model Predator-prey dengan Perilaku Anti Predator serta Efek Allee pada Prey
No full textWe explore a predator-prey model that incorporates both anti-predator behavior by the prey and the Allee effect, where population growth declines at low densities. Four equilibrium points emerge: extinction for both species (E0), two predator extinction points (E1 and E2), and one coexistence point for both populations (E3). While the stability of E0, E2, and E3 depends on the given parameters, E1 is always unstable. We then verified this analysis through numerical simulations using Runge-Kutta method in Python.Kami mempelajari model predator-prey dengan perilaku anti-predator dan efek Allee pada prey. Efek Allee merupakan fenomena ekologi yang menggambarkan penurunan pertumbuhan populasi karena berkurangnya kepadatan suatu populasi spesies, sedangkan perilaku anti predator adalah perilaku prey untuk melindungi diri dari predator. Kami menemukan 4 titik kesetimbangan, yaitu titik kepunahan kedua spesies , dua titik kepunahan predator dan ) dan satu titik koeksistensi kedua spesies . Kestabilan dan tergantung dari parameter yang diberikan, sedangkan titik selalu tidak stabil. Selanjutnya kami melakukan simulasi numerik dengan metode Runge-Kutta menggunakan bahasa pemrograman Python untuk mengkonfirmasi analisis model secara grafis
Forecasting Non-Metal and Rock Mineral (MBLB) Tax Revenue Using the Fuzzy Time Series Markov Chain Method in East Lombok Regency
Get PDFIndonesia is one of the countries that is included in a developing countries. Therefore, the Indonesian Goverment is trying to carry out various developments in various regions. Regional development is one of the Indonesian government’s ways of achieving national goals. In carrying out regional development, of course funds are needed as the main source to support the achievement of national development. The main source of funds obtained by the Government comes from Regional Oroginal Income. One source of Regional Oroginal Income is tax. There are various types of taxes managed by the government in East Lombok Regency. One of them is the Non-Metal Minerals and Rocks, which is a tax on the extraction of non-metallic minerals and rock Tax, which is a tax on the extraction of of non-metallic minerals and rocks from natural sources within or on the surface of the earth for use. This Non-Metal and Rock Mineral tax provides quite large revenues for East Lombok district regional taxes. Non-Metal and Rock Mineral tax income is often not constant, meaning that there is an increases and there is a decreases in the amount of income. For this reason, it is necessary to forecast Non-Metal and Rock Mineral tax revenue to predict income in the future. The method used in this study is the FTS Markov Chain order 1 and order 2. Based on the MAPE indicator, the results of forecasting using the FTS Markov Chain method of order 1 amounted to Rp. 1.117.069.497 with an accuracy of 48,55% with a just good forecasting classification. While the results of forecasting using the FTS Markov Chain method of order 2 amounted to Rp.1.761.652.173 with an accuracy of 39,12% with a just good forecasting classification. If seen from the MAPE value obtained, the forecasting results using the 2nd order FTS Markov Chain are more accurate than using the 1st order Markov Chain FTS method
Mathematical Model of Differential Equations to Population Growth Models with Limited Growth in West Nusa Tenggara Province
Get PDFDifferential equations are often a topic in the field of mathematics which has many applications in mathematical modeling, one of which is population growth. Research on population growth is of course important for an area because the results of this research can be used in issuing policies such as maintaining the availability of agricultural land, places to live, and many others. In this study, the mathematical model of differential equations was used to find a population growth model for the West Nusa Tenggara Province, then the model was verified and calculations were carried out using the Mathematica software. Then a model is generated with the equation () = 3504006 0,012(−1993) which results in a calculation that the population of NTB will continue to grow so that it is necessary to verify the model which produces a logistics growth model
Algebraic Structures and Combinatorial Properties of Unit Graphs in Rings of Integer Modulo with Specific Orders
Get PDFUnit graph is the intersection of graph theory and algebraic structure, which can be seen from the unit graph representing the ring modulo n in graph form. Let R be a ring with nonzero identity. The unit graph of R, denoted by G(R), has its set of vertices equal to the set of all elements of R; distinct vertices x and y are adjacent if and only if x + y is a unit of R. In this study, the unit graph, which is in the ring of integers modulo n, denoted by G(Zn). It turns out when n is 2^k, G(Zn) forms a complete bipartite graph for k∈N, whereas when n is prime, G(Zn) forms a complete (n+1)/2-partites graph. Additionally, the numerical invariants of the graph G(Zn), such as degree, chromatic number, clique number, radius, diameter, domination number, and independence number complement the characteristics of G(Zn) for further research
Pemodelan Tingkat Pengangguran Terbuka di Indonesia Menggunakan Analisis Regresi Data Panel
No full textIndonesia has entered the peak of the demographic bonus which can provide positive and negative impacts for various fields. One of them is in the economic field, namely the increasing number of productive population who are unabsorbed in the world of work and is referred to as an open unemployment. This research was conducted to build a model and to analyze the Open Unemployment Rate, Economic Growth, Provincial Minimum Wage, Level of education, Population growth, Labor Force Participation Rate, Employment, Human Development Index, Poor Residents, Illiterate Population, Average Length of School, Domestic Investment, Foreign Investment, and School Participation Rate, that influence the open unemployment rate in Indonesia using panel data regression analysis with data 2015-2021 from 34 provinces. A fixed effect model with different intercept values for every participant is the best panel data regression model (Fixed Effect Model) that could be found. Based on simultaneously research, it was discovered that every component of the model significantly effect the open unemployment rate. Partially, it was discovered that the following factors significantly effect the open unemployment rate in Indonesia: Employment, Labor Force Participation Rate, Economic Growth, Population Growth, Human Development Index, Poor Population, and Average years of Schooling.Indonesia telah memasuki puncak bonus demografi yang dapat memberikan dampak positif maupun dampak negatif terhadap berbagai bidang. Salah satunya dalam bidang ekonomi yakni semakin banyak populasi penduduk usia produktif yang tidak terserap dalam dunia kerja dan disebut sebagai pengangguran terbuka. Penelitian ini dilakukan untuk membangun model dan menganalisis faktor-faktor yang mempengaruhi tingkat pengangguran terbuka di Indonesia menggunakan analisis regresi data panel. Model regresi data panel terbaik yang diperoleh yakni model pengaruh tetap dengan nilai intersep pada setiap individu berbeda (Fixed Effect Model). Berdasarkan penelitian diperoleh faktor-faktor yang signifikan mempengaruhi Tingkat Pengangguran Terbuka (TPT) di Indonesia yakni Pertumbuhan Ekonomi (), Pertumbuhan Penduduk (), Tingkat Partisipasi Angkatan Kerja (), Penyerapan Tenaga Kerja (), Indeks Pembangunan Manusia (), Penduduk Miskin (), dan Rata-rata Lama Sekolah () dengan koefisien determinasi () sebesar 44,81%