Application of GARCH Forecasting Method in Predicting The Number of Rail Passengers (Thousands of People) in Jabodetabek Region

PT. Kereta Api Indonesia and PT. KAI Commuter Jabodetabek records time series data in the form of the number of train passengers (thousand people) in Jabodetabek Region in 2011-2020. One of the time series methods that can be used to predict the number of train passengers (thousand people) in Jabodetabek area is ARIMA method. ARIMA or also known as Box-Jenkins time series analysis method is used for short-term forecasting and does not accommodate seasonal factors. If the assumption of residual homoscedasticity is violated, the ARCH / GARCH method can be used, which explicitly models changes in residual variety over time. This study aims to model and forecast the number of train passengers (thousand people) in Jabodetabek area in 2021. Based on data analysis and processing using ARIMA method, the best model is ARIMA (1,1,1) with an AIC value of 2,159.87 and with ARCH / GARCH method, the best model is GARCH (1,1) with an AIC value of 18.314. Forecasting results obtained based on the best model can be used as a reference for related parties in managing and providing public transportation facilities, especially trains.

Direct Sums of Prime Subsemimodules

Let be a commutative semiring. A semimodule over a semiring is a fully prime semimodule if each proper subsemimodule of is prime. This research aims to investigate the relationship between a direct sum of prime subsemimodules and , , and a fully prime semimodule.

Determinants of Development Achievements on District/City of Central Java in 2019

In 2019, Badan Perencanaan Pembangunan Nasional (Bappenas) awarded Central Java as the province with the best Perencanaan dan Pembangunan Daerah (PPD). However, if it is reviewed at the district/city level, it shows that there are still many areas that have low development achievements. In accordance with the United Nations Development Programme (UNDP) proposal, the Human Development Index (HDI) is used as an indicator of the achievement of district/city development whose calculations are good enough to describe development from both a social and economic perspective. The large difference in HDI between districts/cities in Central Java and the distribution of development achievements are still centered around the provincial capital, namely Semarang City, this indicates the occurrence of inequality in development achievements at the district/city level in Central Java. Because the observations in this study are districts/cities in Central Java, the linkage between district/city causes spatial autocorrelation. Therefore, spatial regression model is used to determine the model that has spatial autocorrelation. This study aims to determine the achievements of development and its determinants in the districts/cities of Central Java in 2019 using the spatial regression analysis method. From the results of the study, it is known that there is a dependence on development achievements between districts/cities in Central Java which is influenced by the regional capacity factor is characterized by PAD and economic growth; operational resource factors characterized by DAU, DAK and technology; and the level of poverty.

Comparison of M Estimation, S Estimation, with MM Estimation to Get the Best Estimation of Robust Regression in Criminal Cases in Indonesia

Crime incidents that occurred in Indonesia in 2019 based on Survey Based Data on criminal data sourced from the National Socio-Economic Survey and Village Potential Data Collection produced by the Central Statistics Agency recorded 269,324 cases. The high crime rate is caused by several factors, including poverty and population density. Determination of the most influential factors in criminal acts in Indonesia can be done with Regression Analysis. One method of Regression Analysis that is very commonly used is the Least Square Method. However, Regression Analysis can be used if the assumption test is met. If outliers are found, then the assumption test is not completed. The outlier problem can be overcome by using a robust estimation method. This study aims to determine the best estimation method between Maximum Likelihood Type (M) estimation, Scale (S) estimation, and Method of Moment (MM) estimation on Robust Regression. The best estimate of Robust Regression is the smallest Residual Standard Error (RSE) value and the largest Adjusted R-square. The analysis of case studies of criminal acts in Indonesia in 2019 showed that the best estimate was the S estimate with an RSE value of 4226 and an Adjusted R-square of 0.98

Forecasting Stock Price PT. Telkom Using Hybrid Time Series Regression Linear– Autoregressive Integrated Moving Average Model

The hybrid method is a method of combining two forecasting models. Hybrid method is used to improve forecasting accuracy. In this study, the Time Series Regression (TSR) linear model will be combined with the Autoregressive Integrated Moving Average (ARIMA) model. The TSR linear model is used to obtain the model and residual value, then the residual value of the TSR linear model will be modeled by the ARIMA model. This combination method will produce a hybrid TSR linear-ARIMA model. The case study in this research is stock closing price (daily) of PT. Telkom Indonesia Tbk. The stock closing price (daily) of PT. Telkom Indonesia Tbk in 2020 showed an decreasing and increasing trend pattern. The results of this study obtained the best model of hybrid TSR linear-ARIMA (2,1,1) with the proportion of data training and testing is 70:30. In the best model, the MAD value is 56.595, the MAPE value is 1.880%, and the RMSE value is 78.663. It is also found that the hybrid TSR linear-ARIMA model has a smaller error value than the TSR linear model. The results of forecasting the stock price of PT. Telkom Indonesia Tbk for the period 02 January 2021 to 29 January 2021 formed a decreasing trend pattern.

The Primitive-Solutions of Diophantine Equation x^2+pqy^2=z^2, for primes p,q

In this paper, we determine the primitive solutions of diophantine equations x^2+pqy^2=z^2, for positive integers x, y, z, and primes p,q. This work is based on the development of the previous results, namely using the solutions of the Diophantine equation x^2+y^2=z^2, and looking at characteristics of the solutions of the Diophantine equation x^2+3y^2=z^2 and x^2+9y^2=z^2.

Determination of Fractional Chromatic Numbers in the Operation of Adding Two Different Graphs

The development of graph theory has provided many new pieces of knowledge, one of them is graph color. Where the application is spread in various fields such as the coding index theory. Fractional coloring is multiple coloring at points with different colors where the adjoining point has a different color. The operation in the graph is known as the sum operation. Point coloring can be applied to graphs where the result of operations is from several special graphs. In this case, the graph summation results of the path graph and the cycle graph will produce the same fractional chromatic number as the sum of the fractional chromatic numbers of each graph before it is operated.

Optimization of Raw Material Inventory Control CV. Dirga Eggtray Pinrang Using Probabilistic Model with Backorder and Lostsales Condition

This research discusses about the comparison of raw material inventory control CV. Dirga Eggtray Pinrang. It starts with forecasting inventory for the next 12 periods using variations of the time series forecasting method, where the linear regression method provides accurate forecasting results with a Mean Absolute Percentage Error (MAPE) value of 1,9371%. The probabilistic models of inventory control used are the simple probabilistic model, Continuous Review System (CRS) model, and Periodic Review System (PRS) model. The CRS model with backorder condition is a model that provides the minimum cost of Rp. 969.273.706,20 per year compared to another probabilistic model with the largest difference of Rp. 1.291.814,95 per year, with the optimum number of order kg, reorder level kg, and safety stock kg.

Application of the Autoregressive Integrated Moving Average Exogenous (ARIMAX) with Calendar Variation Effect Method for Forecasting Chocolate Data in Indonesia and the United States

Forecasting chocolate consumption is required by producers in preparing the amount of production each month. The tradition of Valentine, Christmas and Eid al-Fitr which are closely related to chocolate makes it impossible to predict chocolate by using the Classical Time Series method. Especially for Eid al-Fitr, the determination follows the Hijri calendar and each year advances 10 days on the Masehi calendar, so that every three years Eid al-Fitr will occur in a different month. Based on this, the chocolate forecasting will show a variation calendar effect. The method used in modeling and forecasting chocolate in Indonesia and the United States is the ARIMAX (Autoregressive Integrated Moving Average Exogenous) method with Calendar Variation effect. As a comparison, modeling and forecasting are also carried out using the Naïve Trend Linear, Naïve Trend Exponential, Double Exponential Smoothing, Time Series Regression, and ARIMA methods. The ARIMAX method with Calendar Variation Effect produces a very precise MAPE value in predicting chocolate data in Indonesia and the United States. The resulting MAPE value is below 10 percent, so it can be concluded that this method has a very good ability in forecasting.

Some Types of Irregular Labeling of Diamond Networks on Ten Vertices

There are three interesting parameters in irregular networks based on total labelling, i.e. the total vertex irregularity strength, the total edge irregularity strength, and the total irregularity strength of a graph. Besides that, there is a parameter based on edge labelling, i.e., the irregular labelling. In this paper, we determined the four parameters for diamond graph on eight vertices.