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Upaya pelestarian anggrek, khususnya anggrek spesies merupakan salah satu kegiatan konservasi lingkungan hidup. Dalam rangka pelestarian lingkungan, lingkungan kampus sudah dipenuhi berbagai pohon-pohon rindang dan tinggi, yang sangat sesuai untuk habitat anggrek hutan. Adanya tanaman-tanaman ini merupakan salah satu upaya konservasi lingkungan, keindahan, dan pengurangan gas CO2. Untuk menambah keindahannya, pohon-pohon besar yang ada di lingkungan taman kampus dapat ditempel berbagai jenis anggrek yang sesuai dengan habitatnya seperti amabilis, retusa, bulbophyllum, aphyllum, dan dendrobium. Anggrek, selain indah dan cantik, juga akan mengurangi kadar CO2 di udara sehingga penanaman anggrek di lingkungan kampus akan berdampak baik terhadap peringkat greenmetric. Tujuan kegiatan pengabdian ini adalah untuk: (1) melestarikan anggrek spesies khususnya amabilis yang merupakan spesies asli Lampung, (2) mengurangi CO2 dan meningkatkan peringkat greenmetric. Kegiatan ini melibatkan tim dosen, mahasiswa, dan staff untuk membantu merawat tanaman anggrek. Tingkat keberhasilan hidup anggrek untuk beradaptasi di lingkungan kampus sangat baik (lebih dari 95%). Partisipasi dan antusiasme masyarakat dan civitas akademika di lingkungan kampus juga sangat baik. Hal ini ditandai dengan pertumbuhan anggrek yang baik dan masih utuhnya plant anggrek yang ditanam.

Many analytical methods can be utilized for multivariate time series modeling. One of the analytical models for modeling time series data with multiple variables is the State Space Model. The data to be analyzed in this study is inflation data from expenditure groups such as processed foods, beverages, cigarettes, and tobacco; and housing inflation for water, electricity, gas, and fuel from January 2001 to December 2021. The aim is to determine the best State Space Model that fits the data for forecasting. In this study, the State Space method will be utilized further with multivariate time series data and represent State Space in Vector Autoregressive (VAR) to determine the relationship between groups of observed variables.

The model of Vector Autoregressive (VAR) with cointegration is able to be modified by Vector Error Correction Model (VECM). Because of its simpilicity and less restrictions the VECM is applied in many studies. The correlation among variables of multivariate time series also can be explained by VECM model, which can explain the effect of a variable or set of variables on others using Granger Causality, Impulse Response Function (IRF), and Forecasting. In this study, the relationship of Energy Used and CO2 will be discussed. The data used here were collected over the year 1971 to 2018. Based on the comparison of some criteria: Akaike Information Criterion Corrected (AICC), Hannan-Quin Information Criterion (HQC), Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC) for some VAR(p) model with p= 1,2,3,4,5, the best model with smallest values of AICC, HQC, AIC and SBC is at lag 2 (p= 2). Then the best model found is VECM (2) and further analysis such as Granger Causality, IRF, and Forecasting will be based on this model.

Understanding the probabilistic or statistical behavior of air concentrations is necessary for the effective management of air pollution, such as PM2.5. Failure to consider the appropriateness of the model can lead to making inferences that are not supported by scientific evidence. The main focus of this article is to find the best statistical distribution in fitting PM2.5 concentrations in the periods of February–June 2018 and February–June 2019 (the periods without COVID-19) and in the period of February–June 2020 (the period with COVID-19) in Jakarta, Indonesia. This article considers making an assessment of the performance of both generalized distributions (e.g., generalized gamma, generalized extreme value, and generalized log-logistic [GLL]) and classical distributions (such as lognormal [LN], gamma, Weibull, log-logistic, and Gumbel) in modeling daily concentrations of PM2.5 in the period of February–June 2020, or the period during which the COVID-19 pandemic is present, in Jakarta. For comparison purposes, this study also analyzed PM2.5 concentrations in the periods of February–June 2018 and February–June 2019. The comparative evaluation of the models of each period of data uses graphical analyses and goodness-of-fit statistics. The results of applications indicate that the generalized distributions fit the data better than do the classical distributions. Particularly, compared with the classical distributions, including the LN model, the GLL distribution is the most appropriate model in fitting PM2.5 concentrations in the periods without and during the period with COVID-19 in Jakarta, Indonesia. © 2021 by the authors;licensee Growing Science, Canada.

The Generalized Gamma distribution is very suitable for modeling data with various forms of hazard (risk) functions, which makes the Generalized Gamma distribution useful in survival analysis. Survival analysis aims are to predict chances of survival, disease recurrence, death, and other events over a period of time. One characteristic of survival data is the possibility of sensors. Let X be the life span of the person being studied and the right censorship time of Cr, X is assumed to be independent with the probability density function f(x), the survival function S(x), and the hazard function h(x). A person's X life span will be known if X is less than or equal to Cr. If X is greater than Cr, the individual X survives or is censored right now. Statistical inference, especially parameter estimation is needed in analyzing empirical data. Obviously the estimation results obtained are expected to be a good estimator, namely to meet the nature of unbiased and minimum variance. This paper will discuss the results of the estimation of Generalized Gamma distribution parameters with type 1 right censored data through simulations using the Expectation Maximization method and the Maximum Likelihood Estimation method. The simulation is conducted by generating data with the sample size: 25, 50, 100, 200, 500, 1000, 1500 and 2000 as well as determining censored data of 10%, 20% and 30% by first setting the parameters used which are obtained from the data of patients with gastric cancer namely α = 1.0649, β = 1,072, θ = 59.766. Based on the results obtained from the simulations on the two estimation methods that the parameter estimation using the Maximum Likelihood Estimation method is better than the Expectation Maximization method because it provides a smaller bias and MSE value where the larger the sample size used, the estimated parameter value will get closer to the parameter in fact. In addition, the Expectation Maximization method can also be used as an alternative estimation of generalized gamma distribution parameters with type 1 right censored data because it has a bias value and MSE approaching the MLE method.

It is well known that a country's economy is very dependent on the export of goods and services produced by that country. This depends on exporting either mining products such as oil and gas or non-oil and gas. This paper will study the data export of oil and gas and data export of non-oil and gas of Indonesian over the years 2008 to 2019. The aim of this study is to obtain the best model that can describe the pattern of the data export of oil and gas and data export of non-oil and gas. From the results of the analysis, researchers found that the best models that can describe the pattern of data export of oil and gas and data export of non-oil and gas are the same, namely: ARMA (2.1) -GARCH (1.1) models. These models for both data are very significant with P-values < 0.0001 and < 0.0001, respectively, R-squares are 0.8797 and 0.7604, respectively and Mean Average Percentage Errors (MAPE) are 12.41 and 6.92, respectively. These models are very reliable, and they can be used to predict (forecast) for the next 12 periods (months).Keywords: Akaike’s Information Criterion, Autoregressive Moving Average, Generalized Autoregressive Conditional Heteroscedasticity, Mean Average Percentage Error.JEL Classifications: C32, Q4, Q47DOI: https://doi.org/10.32479/ijeep.9892

A Graph G (V, E) is said to be a connected graph if for every two vertices on the graph there exist at least a path connecting them, otherwise, the graph is disconnected. Two edges or more that connect the same pair of vertices are called parallel edges, and an edge that starts and ends at the same vertex is called a loop. A graph is called simple if it containing no loops nor parallel edges. Given n vertices and m edges, m ≥ 1, there are many graphs that can be formed, either connected or disconnected. In this research, we will discuss how to calculate the number of connected vertices labeled graphs of order six (isomorphism graphs are counted as one), with a maximum loop of ten without parallel edges.

Application of Path Analysis for causal modeling has been widely used in many areas of studies, such as in social science, education, biology, medical, sociology, and economics. In this study, path analysis is applied to test a relationship model among variables: Foreign Direct Investment (FDI), Industry growth (IND), Energy use (ENR), and Carbon dioxide (CO2) emissions. Aims of this study are to know whether there exist direct effect of Foreign Direct Investment (FDI) to Industry growth (IND), direct effect of Foreign Direct Investment (FDI) and Industry growth (IND) to Energy use (ENR), and direct effect of Industry growth (IND) and Energy use (ENR) to Carbon dioxide (CO2) emissions. Results of analysis show that there is a direct effect of Foreign Direct Investment (FDI) to Industry growth (IND) where the effect is determined as 0.3597; parameter estimate is significant and meaningfulness. There is direct effect of Foreign Direct Investment (FDI) and Industry growth (IND) to Energy use (ENR). Effect of Foreign Direct Investment (FDI) to Energy use (ENR) is identified as 0.2736; parameter estimate is not significant, but the value is still meaningfulness. Direct effect of Industry growth (IND) to Energy use (ENR) is -0.4975; parameter estimate is very significant. There is a direct effect of Industry growth (IND) and Energy use (ENR) to Carbon dioxide (CO2) emissions. Effect of Industry growth (IND) to Carbon dioxide (CO2) emissions is 0.0557; parameter estimate is not significant, but the value is still meaningfulness. Direct effect of Energy use (ENR) to Carbon dioxide (CO2) emissions is 0.9597 where parameter estimate is very significant and meaningfulness.Keywords: path analysis, decomposition of correlation, direct effect, indirect effect, total effectJEL Classifications: C51, Q4, Q43DOI: https://doi.org/10.32479/ijeep.8528

Vector Error-Correction Model (VECM) is a method of statistical analysis frequently used in many studies in time series data of economy, business and finance, and data energy. It is applied across researches due to its simplicity and limited restrictions. VECM can explain not only the dynamic behavior of the relationship among variables of endogenous and exogenous, but also among the endogenous variables. Moreover, it also explains the impact of a variable or a set of variables on others by means of Impulse Response Function and Granger Causality analysis. It can also be used for forecasting multivariate time series data. In this research, the relationship of three share price of energy (from three Asean countries: PGAS Malaysia, AKRA Indonesia, and PTT Thailand) will be studied. The data in this study were collected from October 2005 to August 2019. Based on the comparison of some VECM models, it was found that the best model is VECM (2) with cointegration rank=3. The dynamic behavior of the data is studied through Impulse Response Function (IRF), Granger Causality analysis and forecasting for the next five periods(weeks).Keywords: Cointegration, VAR model, VECM model, Granger Causality, Impulse Response Function, Forecasting.JEL Classifications: C32, Q4, Q47DOI: https://doi.org/10.32479/ijeep.8946

The Minimum Spanning Tree (MST) is one of the famous problems that is used mostly as the backbone in many network design problems. Given a graph G(V,E), where V is the set of vertices and E is the set of edges connecting vertices in V, and for every edge eij there is an associated weight cij ?0. The Multi Period Degree Constrained Minimum Spanning Tree (MPDCMST) is a problem of finding an MST while also considering the degree constrained on every vertex, and satisfying vertices installation requirement on every period. Two algorithms (WWM1 and WWM2) are proposed for solving this problem. GNU OCTAVE is used for coding and visualization. GNU is a recursive acronym for "GNU's Not Unix!", and that name is chosen because it is like Unix but differs from Unix because it is free and contains no Unix code. Those algorithms were implemented using 300 randomly generated problems. Moreover, we compare WWM1 and WWM2 algorithms using existing data from the literature and the results show that WWM2 is the best. ABSTRAK: Minimum Spanning Tree (MST) merupakan salah satu masalah mahsyur yang banyak digunakan sebagai tulang belakang kepada masalah banyak rekaan jaringan. Menerusi graf G(V,E), di mana V adalah himpunan titik dan E adalah himpunan garis yang menghubungkan titik-titik dalam V, dan bagi setiap garis eij terdapat berat berhubung cij ?0, Multi-period Degree Constrained Minimum Spanning Tree (MPDCMST) merupakan masalah dalam menentukan MST, pada masa sama turut menimbangkan kekangan pada setiap titik vertek, dan memenuhi syarat keperluan pemasangan pada setiap detik. Dua algoritma (WWM1 dan WWM2) dicadangkan bagi menyelesaikan masalah ini. GNU OCTAVE digunakan bagi pengaturcaraan dan visualisasi. GNU merupakan suatu singkatan kepada “GNU's Not Unix”, dan nama tersebut dipilih karena ianya seperti Unix, tetapi berbeza dari Unix kerana ia percuma dan tidak mempunyai kod Unix. Algoritma tersebut dilaksana dengan menggunakan 300 masalah terhasil secara rawak. Tambahan, algoritma WWM1 dan WWM2 dibandingkan dengan kajian terdahulu dan hasil kajian menunjukkan WWM2 adalah terbaik.

The vector autoregressive moving average (VARMA) model is one of the statistical analyses frequently used in several studies of multivariate time series data in economy, finance, and business. It is used in numerous studies because of its simplicity. Moreover, the VARMA model can explain the dynamic behavior of the relationship among endogenous and exogenous variables or among endogenous variables. It can also explain the impact of a variable or a set of variables by means of the impulse response function and Granger causality. Furthermore, it can be used to predict and forecast time series data. In this study, we will discuss and develop the best model that describes the relationship between two vectors of time series data export of Coal and data export of Oil in Indonesia over the period 2002–2017. Some models will be applied to the data: VARMA (1,1), VARMA (2,1), VARMA (3,1), and VARMA (4,1). On the basis of the comparison of these models using information criteria AICC, HQC, AIC, and SBC, it was found that the best model is VARMA (2,1) with restriction on some parameters: AR2_1_2=0, AR2_2_1=0, and MA1_2_1=0. The dynamic behavior of the data is studied through Granger causality analysis. The forecasting of the series data is also presented for the next 12 months.Keywords: VARMA model, Information criteria, Granger causality, ForecastingJEL Classifications: C53, Q4, Q47DOI: https://doi.org/10.32479/ijeep.7605

Owing to its simplicity and less restrictions, the vector autoregressive with exogenous variable (VARX) model is one of the statistical analyses frequently used in many studies involving time series data, such as finance, economics, and business. The VARX model can explain the dynamic behavior of the relationship between endogenous and exogenous variables or of that between endogenous variables only. It can also explain the impact of a variable or a set of variables on others through the impulse response function (IRF). Furthermore, VARX can be used to predict and forecast time series data. In this study, PTBA and HRUM energy as endogenous variables and exchange rate as an exogenous variable were studied. The data used herein were collected from January 2014 to October 2017. The dynamic behavior of the data was also studied through IRF and Granger causality analyses. The forecasting data for the next one month was also investigated. On the basis of the data provided by these different models, it was found that VARX (3,0) is the best model to assess the relationship between the variables considered in this work.Keywords: VAR model, VARX model, Granger causality, Impulse Response Function, Forecasting.JEL Classifications: C32, Q4, Q47DOI: https://doi.org/10.32479/ijeep.7223

Small area estimation is defined as a statistical technique for estimating the parameters of a subpopulation with a small sample size. One method of estimating small area parameters is the Empirical Bayes (EB) method. The accuracy of the Empirical Bayes (EB) estimator can be measured by evaluating the Mean Squared Error (MSE). In this study, 3 methods to determine MSE in the EB estimator of the Beta-Bernoulli model will be compared, namely the Bootstrap, Jackknife Jiang and Area-specific Jackknife methods. The study is carried out theoretically and empirically through simulation with R-studio software version 1.2.5033. The simulation results in a number of areas and pairs of prior distribution parameter values, namely Beta, show the effect of sample size and parameter value pairs on the Mean Square Error (MSE) value. The larger the number of areas and the smaller the initial 𝛽, the smaller the MSE value. The area-specific Jackknife method produces the smallest MSE in the number of areas 100 and the Beta parameter value 0.1.

Hukum Islam merupakan salah satu elemen paling penting dalam ajaran Islam. Pengaruh hukum Islam masuk ke dalam bidang-bidang lain dalam studi keislaman. Implikasi hukum Islam yang begitu kuat dalam kehidupan umat Islam, dapat dilihat dari kuatnya perspektif hukum dalam cara pandang umat Islam, untuk melihat problem kehidupan keseharian. Model pembaharuan hukum Islam di Saudi Arabia adalah pembaruan terbatas. Hukum Islam diletakkan berdampingan dengan tata hukum lainnya, yang dijadikan sebagai sumber hukum kedua. Mekanismenyya adalah al-Qur’an dan al-Sunnah berikut penjelasannya merupakan undang-undang langit. Raja berperan sebagai wakil Allah di muka bumi ini dalam menjalankan undang-undangnya.

Air transportation is now a mode of transportation that is often the first choice. Although the transportation costs are relatively expensive, it can save a lot of time to get to the destination. Therefore, predicting the number of aircraft passengers is an interesting thing to study. In this study forecasting the number of aircraft passengers at Raden Intan II Airport using spectral analysis methods. Spectral analysis is used to obtain more complete information about the time series data characteristics to examine the periodicity. After getting the periodicity the data is modeled using the ARIMA Seasonal Method . Based on the analysis results it is known that the best model for forecasting aircraft passengers at Raden Intan II Airport is Seasonal ARIMA (0,1,1) (0,1,1) 3

The aim of this study is to derive the estimates of the parameters of generalized beta of the second kind (GB2 ) distribution by using the maximum likelihood estimation (MLE ). Due to the difficulty in finding the analytical solution by MLE approach, the estimate is determined numerically by using iteration and Newton-Raphson methods. The Newton-Raphson method is used to estimate parameters, to find a confidence interval, to estimate the bias, and to estimate the variance for some difference sample size configuration viz. for n =30,50,100,20nand 500. The estimation of the parametersa, b, p and q attains the values close to the real value of theparameters. If the size of the sample increases, the confidence intervalbecomes narrower and the bias and variance become smaller.

Objectives: To determine the relationship among Price Index Received by Farmer (PIR), Price Index Paid by the Farmers (PIP) and the Farmers' Terms of Trade (FTT) by using the model VECM, and to attempt to know the behavior of (FTT) if there is a shock in variables PIR and PIP. Methods/Statistical Analysis: Vector Error Correction Model (VECM) is a model Vector Autoregressive (VAR) which can be used for data series which are non stationery and have cointegration relationship (long term relationship). The model VECM can also be used to see the movement in one variable to give a response regarding the shock produce by another variable through the graph of Impulse Response Function (IRF). Findings: Based on the data of Farmers' Terms of Trade in Indonesia over the periods from January 2008 to November 2013, we have determined that the best model VECM is VECM order 2 (VECM (2)). Applications: Based on the graph of the Impulse Response Function (IRF) we have established that the response of FTT toward the shock of a price both received and paid by the farmers is fluctuative and temporary over time.

The notion of the sub-exact sequence is the generalization of exact sequence in algebra especially on a module. A module over a ring R is a generalization of the notion of vector space over a field F. Refers to a special vector space over field F when we have a complete inner product space, it is called a Hilbert space. A space is complete if every Cauchy sequence converges. Now, we introduce the sub-exact sequence on Hilbert space which can later be useful in statistics. This paper aims to investigate the properties of the sub-exact sequence and their relation to direct summand on Hilbert space. As the result, we get two properties of isometric isomorphism sub-exact sequence on Hilbert space.

In this experimental study, Senior high school students take the Test of English as a Foreign Language reading comprehension test using test-taking strategies. One test group takes the Test of English as a Foreign Language as a Computer-Based Test (CBT), and the control group takes the Test of English as a Foreign Language as a Paper-Based Test (PBT). Each class consists of 80 senior high school students divided into 2 groups: 40 male and 40 female, respectively. The experiment was conducted during one semester. The statistical analysis used Factorial Design (2x2) using factors of Sex (Male, Female) and Test (CBT, PBT). For multiple comparison analysis, the Tukey’s method was used. To compare the statistics of the students’ pre-test and post-test scores, the paired t-test was used. From the results of analysis using factorial design, it was found that: The mean Test of English as a Foreign Language reading comprehension scores of males and females was significantly different (p-value < 0.0001); the female mean was higher than the male mean; there was no significant difference between the mean scores of CBT and PBT testing; and there was no interaction between sex and test type. From the analysis results of pre-test and post-test scores using the paired t-test, the difference was very significant (p-value < 0.0001). These results indicate that the Test of English as a Foreign Language reading comprehension scores of students in in both groups (experimental and control), are increased.

The Causal Modeling or Path analysis has become a widely-used statistical method in many areas of study, such as in genetics, biology, social science, environmental science, economic, business, finance and sociology. In this study, causal modeling is used to analyze the relationship among variables of important indicators of the electricity company of the Republic of Indonesia. The variables discussed are Total number of Staff or Employees, Electric Power Installed in megawatts, Operating Cost in million rupees, Electric Power Product in megawatts, Electric Power Sales in megawatts, and Sales Revenue in million rupees. The results of analysis show that the proposed causal modeling indicates the relationships among those six important indicators of the electricity company are very significant and meaningful.

Era globalisasi menyebabkan banyak perubahan dalam pengembangan sistem ekonomi, salah satunya adalah data keuangan. Tujuan dari penelitian ini ialah untuk mendapatkan model terbaik dalam menganalisis dan memprediksi data penutupan harga saham mingguan untuk PT Adhi Karya (Persero) Tbk dari September 1990 hingga Januari 2016 yang berjumlah 1314 data. Model yang digunakan adalah model Asymmetric Power Autoregressive Conditional Heteroscedasticity (APARCH). Model terbaik dipilih berdasarkan Akaike Info Criterion (AIC) dan Schwarz Criterion (SC). Dari hasil analisis diperoleh model terbaik yaitu APARCH (1,1) dengan ARIMA (1,1,1) sebagai model rerata bersyarat. Hasil peramalan untuk 7 periode berikutnya menunjukkan bahwa perkiraan tersebut dalam interval kepercayaan 95% yang berarti bahwa hasil peramalan menggunakan model ini dapat dipercaya dalam kisaran 95%. The era of globalization led to many changes in the development of economic systems, one of which is the data that is financially. The purpose of this study is to get the best model in analyzing and predicting weekly stock price closing data for PT Adhi Karya (Persero) Tbk from September 1990 to January 2016 which amounted to 1314 data. The model used is the Asymmetric Power Autoregressive Conditional Heteroscedasticity (APARCH) model. The best models are selected based on Akaike Info Criterion (AIC) and Schwarz Criterion (SC). From the analysis result obtained the best model that is APARCH (1,1) with ARIMA (1,1,1) as conditional average model. The result of forecasting for the next 7 periods shows that the forecast is within a 95% confidence interval which means that the forecasting result using this model can be trusted in the 95% range.

Hakim yang memiliki kompetensi tinggi dalam bekerja, baik pengetahuan, pengalaman maupun keterampilannya maka akan memiliki semangat yang tinggi pula, sehingga tidak akan sulit dalam mencapai target kerja yang telah ditetapkan dan menjadi tanggung jawabnya, hal ini dikaitkan dengan faktor kompetensi dan insentif kerja. Penelitian ini bertujuan untuk mengetahui dan menganalisis pengaruh kompetensi dan insentif kerja kerja secara parsial dan bersama-sama terhadap kinerja hakim pada Pengadilan Tinggi Tanjungkarang. Jenis penelitian ini adalah penelitian kausal yaitu penelitian yang mengambil sampel dari suatu populasi dan menggunakan kuesioner sebagai alat pengumpul data dan analisis data yang digunakan yaitu uji validitas dan reliabilitas, analisis kualitatif dan analisis kuantitatif berupa analisis regresi linier berganda, uji t dan uji F. Berdasarkan hasil dan interpretasi maka dapat disimpulkan bahwa kompetensi berpengaruh terhadap kinerja hakim pada Pengadilan Tinggi Tanjungkarang, insentif kerja berpengaruh terhadap kinerja hakim pada Pengadilan Tinggi Tanjungkarang serta kompetensi dan insentif kerja berpengaruh terhadap kinerja hakim pada Pengadilan Tinggi Tanjungkarang. Saran yang hendak penulis sampaikan dalam penelitian ini yaitu hendaknya Ketua Pengadilan Tinggi Tanjungkarang mengikutsertakan hakim pada kegiatan pendidikan dan pelatihan (Diklat) teknis komputerisasi secara bergantian dan terus menerus, sehingga hakim memiliki keterampilan yang dapat diandalkan.

The Constant Conditional Correlation-Generalized Autoregressive Conditional Heteroscedasticity (CCC-Garch) model as one of the multivariate time series models is used to model economic variables, especially in stock price data with high volatility characteristics that result in heterogeneous variations. The higher the volatility, the higher the level of uncertainty of the stock returns that can be obtained. The CCC-Garch Multivariate model is the simplest model in its class. The principle of this model is to decompose the conditional covariance matrix into conditional standard deviation and correlation. In this study, we will discuss and determine the best model that can describe the relationship between two vector data timeseries, namely stock return data for companies engaged in mining and construction in Indonesia, namely United Tractor Tbk (UNTR) and Petrosea Tbk (PTRO) where the data is the daily stock return data for the period July 2015 to August 2020. Several models that involve modeling the mean and variance with CCC-GARCH parameterization are applied to data such as the VAR (1)-Garch (1,1), VAR (2)-Garch (1) model., 1), VAR (3) Garch (1,1) and VAR (4)-Garch (1,1). The result was that the VAR (1)-Garch (1,1) model was selected as the best model with the criteria for selecting the AICC, SBC, AIC and HQC models. The dynamic behavior of both UNTR and PTRO stock return variables is explained by Granger Causality and Impulse Response. Furthermore, the forecasting of this data was carried out for some time in which the VAR (1)-Garch (1,1) model which was selected as the best model was only suitable for forecasting in a short time.

Vector Error Correction Model is a cointegrated VAR model. This idea of Vector Error Correction Model (VECM), which consists of a VAR model of the order p - 1 on the differences of the variables, and an error-correction term derived from the known (estimated) cointegrating relationship. Intuitively, and using the stock market example, a VECM model establishes a short-term relationship between the stock prices, while correcting with the deviation from the long-term comovement of prices. An Impulse Response Function traces the incremental effect of a 1 unit (or one standard deviation) shock in one of the variables on the future values of the other endogenous variables. Impulse Response Functions trace the incremental effect of the marketing action reflected in the shock. The data used in this analysis are 4 (four) daily plantation stocks prices in Indonesia with time period of January to July in three years which are 2018, 2019, and 2020. The objective of this study is to determine the relationship among 4 (four) stocks prices with VECM and to know the behaviour of each stocks prices with Impulse Response.

ARIMA method is one method that can be used in predicting the movement of company shares. This study aims to obtain a time series model with the ARIMA method and predict stock price data of PT Unilever Indonesia Tbk from January 2020 to June 2020. The best model that fits the data based on the MSE value is the ARIMA(1,1,1) model. The ARIMA model (1,1,1) shows a match between real data and the predicted value. This model is then used for forecasting the next 14 days. Data on UNVR stock price from January 2020 to June 2020 are below 8000, this seems to correlate with the current conditions, namely the Covid-19 pandemic. Forecasting for the next 14 days (two weeks) from July 1, 2020 to July 14, 2020, the forecast values have a trend decrease, the trend of PT. Unilever Indonesia Tbk has been going down since January 2020. This seems to have occurred as an implication of the Covid-19 pandemic from January 2020 to the present.

If for every pair of vertices in a graph G(V,E) there exist minimum one path joining them, then G is called connected, otherwise the graph is called disconnected. If n vertices and m edges are given then numerous graphs are able to be created. The graphs created might be disconnected or connected, and also maybe simple or not. A simple graph is a graph whose no paralled edges nor loops. A loop is an edges that connects the same vertex while paralled edges are edges that connecting the same pair of vertices. In this research we will discuss the formula to count the number of connected vertex labeled order six graph containing at most thirty edges and may contain fifteen parallel edges without loops.

The Vector Autoregressive (VAR) model is a statistical model that can be used for modeling multivariate time series data which is commonly applied in the fields of finance, management, business and economics. However, economic data, especially return values, have quite high data fluctuations, so we need to add the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model in the analysis to obtain efficient results. This study will discuss the formation of the best model for multivariate time series data, namely return data of PT. Indofarma Tbk. (INAF) and PT. Kimia Farma Tbk. (KAEF) from June 2015 to July 2020, where data retuned for the two variables tended to have a high volatility shock at some time and low volatility at other times which characterizes the data as having an ARCH effect so that the GARCH model will be used in this analysis, namely the BEKK-model. GARCH. This model proposes a new parameterization which is easily given a restriction, namely the requirement that H_t must be positive for all values of ε_t and x_t in sample room. Based on the selection of the best model using the AICC, HQC, AIC and SBC criteria, it is found that the VAR (1)-GARCH (1,1) model is the best model for the data used. Then this research will also examine the behavior and relationship between INAF and KAEF based on Granger Causality and Impulse Response. In addition, based on the forecasting results of the VAR (1)-GARCH (1,1) model, it shows that this model is good for short-term forecasting.

Multivariate time series are widely used in various fields such as finance, economics, and the stock market. One analysis model that is widely used for multivariate time series data is the VAR model. Vector autoregressive (VAR) is a model used to describe the relationship between several variables. The VAR model provides an alternative approach that is very suitable for forecasting purposes and is very suitable for solving economic data problems. The variables used in this study consisted of endogenous variables with closing prices of ICBP and INDF shares and exogenous variables with exchange rates collected from January 2017 to July 2020. In this study, the best model, VARX (1,0), was obtained. also the relationship between variables through the impulse response function and granger causality. Furthermore, forecasting is also carried out for the next 30 days using the best model, VARX (1,0).