Mathematical Journal of Modelling and Forecasting

The Introduction of Strassen's Algorithm and Application to 2^n Matrix Multiplication

Davina Anjelia — 2025-06-30

Abstract. In matrix calculation operations, especially the process of square matrix multiplication, as the order of the matrix increases, the level of accuracy required also increases. Manual calculation is prone to errors and takes a long time, especially for large order matrices. These problems can be overcome by using the Strassen algorithm. Strassen's algorithm views a matrix as a 2×2 matrix because it has four elements. Square matrix multiplication using the Strassen algorithm can be an alternative solution because the Strassen algorithm only contains seven multiplication processes. So, applying the Strassen algorithm to square matrix multiplication will be an alternative in accelerating the multiplication process, especially for matrices of a large order. This research discusses how the Strassen algorithm is formed and its application to the square matrix multiplication of order . Strassen's algorithm is obtained by transforming the elements of the product matrix C. Algebraic identity transformation is done by applying the properties that apply to the calculation operation without changing the original value. Using Strassen's Algorithm in the square matrix multiplication process can be an alternative in accelerating the multiplication process because Strassen's algorithm summarises the multiplication process into seven steps, compared to multiplication in general, which requires eight steps.

Earthquake Point Clustering in Sumatra Island using Spatio-Temporal Density-Based Spatial Clustering Application with Noise (ST-DBSCAN) Algorithm

Muthiara Hazimah Putri — 2025-06-30

Abstract. Earthquakes are one of the natural disasters that often occur in Indonesia, especially on the island of Sumatra. Earthquakes become a frightening spectre because they cannot be predicted when they will come, where they will be located, and how strong the vibrations are, so they often cause damage and casualties. To minimise losses due to earthquakes, it is necessary to divide areas easily affected by earthquakes. One method that can be used to divide these areas is clustering techniques. This study uses a clustering method, namely Spatio Temporal-Density Based Spatial Clustering Application with Noise (ST-DBSCAN), on the dataset of earthquake points on the island of Sumatra in 1917-2023. This method uses a spatial distance parameter (ε_1= 0.28), temporal distance parameter (= 180), and minimum number of cluster members (MinPts = 7) with a silhouette coefficient of 0.0991, resulting in 145 clusters with 15 large clusters and 4922 noises. The epicentres are primarily located in Siberut Island, Tanah Bala Island and its surroundings, the Indian Sea opposite Nias Island, the Sea around the Mentawai Islands, Enggano Island and its environs, Simaulue Regency, and Enggano Island and the Sea around it. The most common type of spatio-temporal pattern found is the occasional pattern type.

Strategy for Enhancing GRU-RNN Performance through Parameter Optimization

Hermansah — 2025-06-30

This study examines the selection of optimal parameters in the Gated Recurrent Unit-Recurrent Neural Network (GRU-RNN) model for forecasting inflation in Indonesia. Accurate forecasting requires precise model parameter adjustments, especially for time-series data, which can be either linear or non-linear. The study evaluates several parameters, including learning rate, number of epochs, optimization methods (Stochastic Gradient Descent (SGD) and Adaptive Gradient (AdaGrad)), and activation functions (Logistic, Gompertz, and Tanh). The results show that the best combination consists of the SGD optimization method, logistic activation function, a learning rate of 0.05, and 450 epochs, which delivers the best performance by minimizing errors and achieving high prediction accuracy. When compared to other forecasting models such as Exponential Smoothing (ETS), Autoregressive Integrated Moving Average (ARIMA), Feedforward Neural Network (FFNN), and Recurrent Neural Network (RNN), the GRU-RNN model shows significant superiority. Additionally, the Logistic activation function proves to be more effective in maintaining stability and prediction accuracy, while the use of the Adaptive Gradient (AdaGrad) method results in lower performance. These findings underscore the GRU-RNN model's ability to handle non-linear time-series data and provide insights for developing more accurate and efficient forecasting models in the future.

Forecasting the Saudi Riyal to Indonesian Rupiah Exchange Rate Using ARIMA

Dina Friska — 2025-06-30

A Currency exchange rate is an essential indicator in a country's economy. The exchange rate of a country's currency constantly fluctuates against another country's currency at any time, such as the riyal exchange rate against the rupiah. There are several methods to determine the movement of the currency exchange rate and to forecast time series data, such as Autoregressive Integrated Moving Average (ARIMA). ARIMA is a time series data forecasting method that can handle data that is not stationary to the mean and variance, such as the riyal exchange rate against the rupiah, which fluctuates irregularly. This study will forecast the riyal exchange rate against the rupiah at Bank Indonesia. The data used is daily data. The R Studio program studies the minimum AIC value to select the best model. The ARIMA (2,1,0) model is the best in forecasting the Saudi Arabian Riyal exchange rate (SAR) against the Indonesian rupiah (IDR) with an estimated forecast error of 0.26%.

Forecasting Rainfall in Padang Panjang City Using Fuzzy Time Series Cheng

Tasya Putri Pratama — 2025-06-30

Rainfall is essential in many areas of life, including agriculture, water resource management, and disaster mitigation. Padang Panjang is one of the cities with high rainfall. Rainfall varies throughout the year, affecting agriculture and people's livelihoods. Therefore, accurate rainfall estimation is required to support effective planning and management. This study aims to forecast the amount of rainfall in Padang Panjang City from January 2020 to November 2024 using the fuzzy time series method of the Cheng model. The data is on the monthly rainfall amount from January 2020 to November 2024, obtained from the BMKG Padang Pariaman Climatology Station. The stages in the fuzzy time series Cheng model are forming the universe set, forming intervals, fuzzifying the data, analyzing Fuzzy Logical Relationship (FLR) and Fuzzy Logical Relationship Group (FLRG), determining the weight of the relationship, forecasting, and measuring the accuracy of predicting using Mean Absolute Percentage Error (MAPE). The forecasting results were validated using MAPE, with a value of 41%, which indicates that the model is feasible. The forecasting results for the following three periods are December 2024 high rainfall, January 2025 medium rainfall, and February 2025 high rainfall. This research shows that the fuzzy time series method of the Cheng model can be used as an alternative means of forecasting time series data.

Risk Comparison in Optimal Portfolios: A Study of Value at Risk (VaR) and Tail Value at Risk (TVaR)

Turnika Afdatul Rafni — 2025-06-30

Considering investment risk is something that investors must do before deciding to invest; measuring risk provides an opportunity for investors to get the desired return and minimize losses. This study compares Value at Risk (VaR) and Tail Value at Risk (TVaR) methodologies for measuring portfolio risk. VaR is a commonly used method that provides the maximum loss at a certain confidence level and period. However, VaR is not an effective measure of risk because it does not satisfy one of the axioms of coherent risk measures, i.e., subadditivity. Subsequently, the TVaR measure emerged, which satisfies all the axioms of coherent risk measures, thereby providing a good and effective measure of risk. The optimal portfolio will be formed using the Single Index model, simplifying the Markowitz portfolio model. The Composite Stock Price Index will be the only factor influencing other stocks in this model. The data used data from stocks that were consistently listed on the IDX30 index from 24/10/2022 to 25/10/2024. Based on the result of the analysis of data, the optimal portfolio consists of 5 stocks, i.e., PT Bank Mandiri (BMRI.JK), PT Indofood Sukses Makmur (INDF.JK), PT Bank Central Asia (BBCA.JK), PT Bank Negara Indonesia (BBNI.JK), and PT Barito Pacific (BRPT.JK). Risk measures were compared on the optimal portfolio, using a confidence level of 1-α=95%, with a daily time period, and an initial investment capital of IDR 1 billion. The estimated VaR risk measure is IDR 15.38 million, while TVaR reaches IDR 23.25 million.

Enhancing Oil Field Investment Decisions Using Spiral Dynamics Optimization

Reni Humairah — 2025-06-30

Investment is an activity in the present to obtain profits in the future. One method of investment assessment is calculating Net Present Value (NPV) using Discounted Cash Flow (DCF). To determine the right time to carry out an investment in order to obtain maximum profits, it is necessary to determine a time limit for when the investment should be carried out or not. Then, the threshold curve (optimal implementation time limit) for the investment will first be determined. After obtaining the threshold curve for each investment option, the NPV value for each investment option will then be determined. The best investment choice is the one that provides the highest NPV value. The metaheuristic method is an effective optimization method for determining the optimal investment implementation time limit (threshold curve). One metaheuristic method for determining threshold curves is the Spiral Dynamics Optimization algorithm developed by Kenichi Tamura and Keiichiro Yasuda, a search algorithm inspired by phenomena in nature such as water speed, air pressure speed, Nautilus Shells, and spiral galaxy shapes. The results of this research are areas that are above the threshold curve, which can implement the project, while areas that are below the curve are not recommended for implementing the project.