EIGEN MATHEMATICS JOURNAL

Optimization of Classification Algorithms Performance with k-Fold Cross Validation

Moch. Anjas Aprihartha — 2024-09-20

Supervised learning is a predictive method used to make predictions or classifications. Supervised learning algorithms work by building a model using training data that includes both independent and dependent variables. Several methods for building classification include Logistic Regression, Naive Bayes, K-Nearest Neighbor (KNN), decision tree, etc. The lack of capacity of a classification algorithm to generalize certain data can be associated with the problem of overfitting or underfitting. K-fold cross-validation is a method that can help avoid overfitting or underfitting and produce a algorithm with good performance on new data. This study will test the Naive Bayes, K-Nearest Neighbor (KNN), Classification and Regression Tree (CART), and Logistic Regression methods with k-fold cross-validation on two different datasets. The values of k set for cross-validation are 2, 3, 5, 7, and 10. The analysis results concluded that each classification algorithm performed best at 10-fold cross-validation. In DATA 1, the Naive Bayes algorithm has the highest average accuracy of 0.67 (67%) and the error rate is 0.33 (33%), followed by the CART algorithm, KNN, and finally logistic regression. While DATA 2, the KNN algorithm has the highest average accuracy of 0.66 (66%) and an error rate of 0.34 (34%), followed by the CART algorithm, Naive Bayes, and finally logistic regressionbut can be a reference if you want to predict the growth direction of the accommodation and food service activities sector.

Nowcasting of Indonesia's Gross Domestic Product Using Mixed Sampling Data Regression and Google Trends Data

Niken Yuliana — 2024-09-20

This study aims to compare the results of the GDP nowcasting of the accommodation and food service activities sector without and with the pandemic time using the MIDAS method. The MIDAS method is an econometric approach used to predict economic development using real-time available high-level and low-frequency data. In this study, Google Trend acts as a predictor variable consisting of 16 search categories which are then reduced by Principal Component Analysis, resulting in several principal components. For GDP data, the data period collected is Quarter I 2010 to Quarter I 2023. This period will later be partitioned into the period before the COVID-19 pandemic, namely Quarter I 2010 to Quarter IV 2019 and a combined period, namely Quarter I 2010 to Quarter I of 2023. This partition was carried out to see the performance and sensitivity of the model before and after the shock due to the COVID-19 pandemic. From the models that have been made, nowcasting is carried out and it is found that the RMSE and MAE values for the pre-pandemic model are smaller than the combined model. The RMSE values for each of the pre-pandemic and combined models were 0.005753 and 0.056032 and the MAE values were 0.00359 and 0.048976 for the pre-pandemic and combined models. However, from this study it is not advisable to make predictions on the nominal GDP of the accommodation and food service activities sector because the results of the nowcasting predictions are still far from the actual value, but can be a reference if you want to predict the growth direction of the accommodation and food service activities sector.

Comparison of Several Univariate Time Series Methods for Inflation Rate Forecasting

Salfina Salfina — 2024-09-20

Forecasting inflation is very crucial for a country because inflation is one of indicator to measure development of the country. This study aims to evaluate the effectiveness of three univariate time series methods i.e., ARIMA (Autoregressive Integrated Moving Average), Double Exponential Smoothing (DES), and Trend Projection (TP), in forecasting Indonesia’s monthly inflation rates using data from 2018 to 2022. The analysis identifies DES as the most accurate method, evidenced by its lowest Root Mean Square Error (RMSE) value of 2.9296, outperforming ARIMA and TP, which have RMSE values of 13.1479 and 3.47053, respectively. Consequently, DES was selected as the preferred model for forecasting inflation over the next 36 month, with the forecasts indicating a consistent downward trend in inflation throughout the year. While these findings highlight DES's effectiveness, the study also acknowledges limitations, including its reliance on univariate models that do not incorporate other economic variables, and the potential limitations of the dataset’s specific time frame. To address these limitations, future research should consider multivariate models, integrate machine learning techniques, and conduct scenario analyses to improve forecast accuracy and robustness. Despite these constraints, the study provides valuable insights into inflation forecasting in Indonesia, offering a practical tool for policymakers and contributing to more informed economic decision-making.

Algebraic Structures and Combinatorial Properties of Unit Graphs in Rings of Integer Modulo with Specific Orders

Sahin Two Lestari — 2024-09-20

Unit 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.

Forecasting the Volatility of Tuna Fish Prices in North Sumatra using the ARCH Method in the Period January - April 2024

Riska Multiyaningrum — 2024-10-03

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.

Application of the Average Based Fuzzy Time Series Lee Method for Forecasting World Gold Prices

Husnul Khotimah — 2024-10-15

Gold is a investment that investors are interested in because it has relatively low risk and gold investment is not affected by inflation. Gold prices always change from time to time, so it is necessary to forecast gold prices as a basis for investors in making decisions. The forecasting method used in the fuzzy time series lee method. The purpose of this research is determine the world prices and determine the accuracy of the gold price forecasting value ortained using fuzzy time series lee method. The results of this research are forecasting gold prices in the period November 20, 2023 of US$ 63,89/grams and relatively the level of forecasting accuracy based on MAPE value of 0,540091% included in the very good criteria in forecasting gold prices.

Mathematical Model of Differential Equations to Population Growth Models with Limited Growth in West Nusa Tenggara Province

Nuzla Af'idatur Robbaniyyah — 2024-12-13

Differential 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 (𝑡) = 3504006 𝑒^{0,012(𝑡−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.

The Decision on Selecting the Best Laptop Using Analytical Hierarchy Process and Simple Additive Weighting Method at the Faculty of MIPA University of Mataram

Rifdah Fadhilah — 2024-12-13

Laptops 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.

Numerical Analysis of Mathematical Model for Diabetes Mellitus Disease by Using Adam-Bashfort Moulton Method

Nuzla Af’idatur Robbaniyyah — 2024-12-14

Diabetes mellitus is a metabolic disorder characterized by elevated blood glucose levels, known as hyperglycemia. The objective of this study is to develop a mathematical model of diabetes mellitus. The model will be analyzed in terms of its equilibrium points using the Adam-Bashforth Moulton numerical method. The numerical method that used is a multistep method. The predictor step employs the Runge-Kutta method, while the corrector step uses the Adam-Bashforth Moulton method. The mathematical model of diabetes mellitus is categorized into two classes: uncomplicated diabetes mellitus and complicated diabetes mellitus. The resulting model identifies two equilibrium points: the endemic equilibrium point (complicated) and the disease-free equilibrium point (uncomplicated). The eigenvalues of these equilibrium points are positive real numbers and negative real numbers. Therefore, the stability of the system is found to be unstable and asymptotically stable, indicating that the population of individuals with uncomplicated diabetes mellitus will continue to rise, whereas the population with complications will not increase significantly over time.

Stock Portfolio Optimization Using Single Index Model (SIM) with Exponentially Weighted Moving Average (EWMA) Approach

Ainul Mutmainna — 2024-12-14

The 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.