Claim Missing Document
Check
Articles

Peramalan Return Saham Subsektor Perbankan Menggunakan Model ARIMA-GARCH Fadhilah, Dila Nur; Kankan Parmikanti; Budi Nurani Ruchjana
Jurnal Fourier Vol. 13 No. 1 (2024)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/fourier.2024.131.1-19

Abstract

Subsektor perbankan berperan penting dalam meningkatkan iklim investasi dan pertumbuhan pasar modal di Indonesia melalui penerbitan dan penjualan saham, yang turut berkontribusi dalam pertumbuhan ekonomi negara. Peramalan return harga saham berfungsi untuk meminimalisir kerugian yang diakibatkan oleh fluktuasi. Namun, fluktuasi ini dapat menyebabkan terjadinya heteroskedastisitas yang tidak dapat ditangani oleh pemodelan time series biasa, seperti Autoregressive Integrated Moving Average (ARIMA) sehingga membutuhkan model Generalized Autoregressive Conditional Heteroskedasticity (GARCH) untuk menangani volatilitas terkait heteroskedastisitas. Oleh karena itu, tujuan penelitian ini adalah mengkaji model gabungan ARIMA dan GARCH berupa ARIMA-GARCH dan menaksir parameter menggunakan metode Maximum Likelihood Estimation (MLE). Model ARIMA-GARCH diterapkan pada data harga penutupan saham harian Bank Rakyat Indonesia (Persero) Tbk (BBRI) pada periode 1 Februari 2019 hingga 2 Januari 2024. Hasil penelitian menunjukkan bahwa model terbaik dalam peramalan return harga saham adalah model ARIMA (2,0,2)-GARCH (1,1) dan menghasilkan nilai Root Mean Square Error (RMSE) sebesar 0,01628. Kemudian, hasil peramalan menunjukkan bahwa volatilitas meningkat dari periode pertama hingga periode ke enam.
Spatial Analysis of Dengue Disease in Jakarta Province Sobari, Muhamad; Jaya, I Gede Nyoman Mindra; Ruchjana, Budi Nurani
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v7i4.17423

Abstract

Dengue disease is a virus-borne illness spread by the bite of the female Aedes aegypti mosquito. Jakarta Province has a vulnerability to dengue disease due to high population density and percentage of urban slum households. This study applied a spatial autoregressive (SAR) model to identify the risk factors that affect the number of dengue disease cases in Jakarta Province. The spatial dependency was accounted for using the queen contiguity spatial weight matrix. The number of flood-prone points, the number of slum neighborhood associations, the population density, the number of hospitals and the number of public health centers per 1,000 population and spatial lag significantly impact the number of dengue disease cases in Jakarta Province. When dengue disease cases increase in one sub-district, the number of dengue disease cases in the sub-districts around it will increase as well because of the positive and significant spatial lag coefficient. Based on the direct impact, each addition of one percent of flood-prone points in one sub-district will increase the number of dengue disease cases in that sub-district by 3.86 cases
Penerapan Perangkat Lunak RStudio untuk Penaksiran Parameter Model Spatial Autoregressive Salsabil, Tsuroyya; Kusuma, Dianne Amor; Ruchjana, Budi Nurani
KUBIK Vol 8, No 1 (2023): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v8i1.30037

Abstract

Research and analysis that are not only based on time (temporal) but also on space (spatial) require tools in the form of software to ensure that the data analysis and processing yield good, fast, and accurate results. One of the software tools that can be used for this purpose is RStudio software. The advantages of RStudio include being open-source software (OSS), which can be used freely without cost, and it has many packages and functions that can facilitate data processing. One of the spatial-based analyses is spatial data analysis. The structure within RStudio allows users to call functions related to spatial data analysis, perform computations with sparse matrices (matrices with many zero values), such as spatial weight matrices, estimation of spatial model parameters, and so on. This research examines the application of RStudio software in estimating the parameters of a first-order Spatial Autoregressive (SAR) model using the Maximum Likelihood Estimation (MLE) method on the data of the designation of Intangible Cultural Heritage (ICH) in Indonesia. Based on the results of applying RStudio software, a first-order SAR model with a Queen contiguity weight matrix for the categories of Traditional Customs, Rituals, and Celebrations (TCRC) and Performing Arts (PA) with the minimum Akaike Information Criterion (AIC) value and maximum pseudo- value was obtained for predicting the designation data of ICH in Indonesia. The application of RStudio software to the first-order SAR model for the designation data of ICH in Indonesia speeds up and simplifies calculations, making it suitable as a recommendation for relevant agencies such as the Department of Culture, Tourism, Youth, and Sports (Disbudparpora). 
Penerapan Model Geographically Weighted Regression pada Data Penetapan Warisan Budaya Takbenda di Indonesia Pratomo, Firdaus Ryan; Kusuma, Dianne Amor; Ruchjana, Budi Nurani
KUBIK Vol 9, No 1 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v9i1.33492

Abstract

Intangible Cultural Heritage (WBTb) determination data in Indonesia is a cultural investment that needs to be preserved. One of the efforts to preserve WBTb is to determine the cultural preservation factors that influence the WBTb determination data in Indonesia. These factors include Percentage of Population Watching Performances/Art Exhibitions (PPWP), Percentage of Population Using Regional Languages (PPURL), and Percentage of Households Using Traditional Products (PHUTP). However, the different cultural wealth in each province results in spatial heterogeneity, resulting in differences in the determination of cultural preservation factors in each province. This determination can be done with the Geographically Weighted Regression (GWR) model. This study aims to apply the GWR model with Fix Gaussian Kernel, Fix Bisquare Kernel, and Fix Tricube Kernel weighting to determine cultural preservation factors in WBTb determination data in Indonesia so that it can be known what cultural preservation factors are most influential in each region. The research findings show the existence of spatial heterogeneity only in the category of WBTb designation data for Performing Arts (PA) and Oral Expression Tradition (OET), as well as different GWR models in each province that reflect differences in cultural preservation factors. Evaluation with the coefficient of determination shows that the GWR model with the Fix Gaussian Kernel weighting function is the best model for the PA category. 
PENERAPAN METODE UNIVERSAL KRIGING (UK) UNTUK PREDIKSI KONSENTRASI PARTICULATE MATTER 2.5 (PM2.5) DI KOTA BANDUNG Putri, Salsabila Eka; Kusuma, Dianne Amor; Ruchjana, Budi Nurani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 14 No 2 (2020): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (910.837 KB) | DOI: 10.30598/barekengvol14iss2pp279-292

Abstract

The tendency of increasing industrial and population activities in the city of Bandung causes a decrease in air quality. One material that causes air pollution which is very dangerous for health is particulate matter 2.5 (PM2.5). Efforts to control and overcome PM2.5 concentration are carried out through measurements in several locations. However, due to limitations of measuring devices and costs, so not all locations in the city of Bandung can be measured PM2.5 concentration. PM2.5 concentration data tends not to be stationary. Therefore it is necessary to interpolate the PM2.5 concentration data using the Universal Kriging method. In this paper, the Universal Kriging method can be applied to predict PM2.5 concentrations in locations that are not sampled because the observed PM2.5 concentration data are spatial data that have different PM2.5 concentrations at each location. Data were analyzed with the help of software R 3.5.3 and ArcGIS 10.4 to create contour maps. Based on the prediction results of PM2.5 concentrations at locations that were not sampled, obtained a first order trend equation is better used to predict PM2.5 concentrations because it has a minimum Universal Kriging error variance value compared to the second order trend equation. The results showed that the location with high PM2.5 concentration was in the northwest of Bandung City. Contour maps show locations that have low to high PM2.5 concentrations
Integrating Spatial Autoregressive Exogenous with Ordinary Kriging for Improved Rainfall Prediction in Java: Enhancing Accuracy with Climate Variables and Spatial Autocorrelation Najwa, Sandrina; Pratiwi, Dhanti Aurilia; Ahdian, Muhammad Rhafi; Indriani, Ayu; Mindra, I Gede Nyoman; Falah, Annisa Nur; Ruchjana, Budi Nurani
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 7, No 1 (2025)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v7i1.42070

Abstract

Indonesia is a tropical country with high rainfall influenced by its archipelagic geography and phenomena like El Niño and La Niña. According to the Meteorology, Climatology, and Geophysics Agency (BMKG), La Niña can increase Indonesia's monthly rainfall by 20-40% above normal. Despite numerous existing spatial interpolation methods, there remains a significant research gap in accurately predicting rainfall at unsampled locations, specifically when considering both spatial autocorrelation and multiple climate variables simultaneously. This research proposes Spatial Autoregressive Exogenous Kriging (SAR-X Kriging), a novel hybrid approach that integrates the SAR-X model with Ordinary Kriging to enhance rainfall prediction accuracy. Unlike conventional methods, SAR-X Kriging explicitly captures both spatial dependence and the influence of external climate factors, improving predictive performance. SAR-X Kriging first models spatial dependencies between locations and incorporates exogenous climate variables (surface pressure, air temperature, humidity, wind speed, and solar radiation) to enhance prediction accuracy. It also applies kriging for spatial interpolation. This method was chosen for its robustness in capturing spatial dependence and external influences. The analysis revealed significant spatial dependence across districts/cities in Java Island based on the Moran's Index test. The best SAR-X model, utilizing air temperature and wind speed as exogenous variables, achieved a p-value of 6.0352 × 10-9. Predictions using SAR-X Kriging yielded the lowest Mean Absolute Percentage Error (MAPE) of 3.82%, outperforming the standalone SAR-X method MAPE 4.68% and the Ordinary Kriging method MAPE 3.86%. Practically, these results provide reliable rainfall predictions, enabling better climate-informed decision-making in water resource management, agricultural planning, and flood prevention strategies in Java.Keywords: Climate; Kriging; MAPE; Rainfall; SAR-X. AbstrakIndonesia merupakan negara tropis dengan curah hujan tinggi yang dipengaruhi oleh kondisi geografis kepulauan serta fenomena alam seperti El Niño dan La Niña. Menurut Badan Meteorologi, Klimatologi, dan Geofisika (BMKG), La Niña mampu meningkatkan curah hujan bulanan Indonesia hingga 20-40% di atas normal. Meskipun terdapat berbagai metode interpolasi spasial yang telah dikembangkan, masih terdapat kesenjangan penelitian dalam menghasilkan prediksi curah hujan secara akurat di lokasi yang tidak tersampel, terutama ketika mempertimbangkan secara bersamaan ketergantungan spasial serta pengaruh dari berbagai variabel iklim. Penelitian ini mengusulkan metode bernama Spatial Autoregressive Exogenous Kriging (SAR-X Kriging), sebuah pendekatan hybrid baru yang mengintegrasikan model SAR-X dengan metode Ordinary Kriging untuk meningkatkan akurasi prediksi curah hujan. Tidak seperti metode konvensional, SAR-X Kriging secara eksplisit menangkap ketergantungan spasial serta pengaruh faktor iklim eksternal, sehingga meningkatkan kinerja prediktif. SAR-X Kriging bekerja dengan memodelkan terlebih dahulu ketergantungan spasial antar lokasi, kemudian memasukkan variabel eksogen berupa tekanan permukaan, suhu udara, kelembaban, kecepatan angin, dan radiasi matahari untuk meningkatkan akurasi prediksi, serta terakhir menerapkan teknik kriging untuk interpolasi spasial. Metode ini dipilih karena mampu menangkap secara lebih baik ketergantungan spasial sekaligus pengaruh variabel eksternal dibandingkan metode konvensional. Hasil analisis menunjukkan adanya ketergantungan spasial yang signifikan antar kabupaten/kota di Pulau Jawa berdasarkan uji Moran’s Index. Model SAR-X terbaik diperoleh dengan variabel suhu udara dan kecepatan angin, mencapai nilai p-value sebesar 6.0352 × 10-9. Prediksi menggunakan SAR-X Kriging menghasilkan Mean Absolute Percentage Error (MAPE) sebesar 3,82%, mengungguli metode SAR-X yaitu MAPE 4,68% dan metode Ordinary Kriging yaitu MAPE 3,86%. Secara praktis, hasil ini dapat meningkatkan kualitas prediksi curah hujan yang bermanfaat dalam pengelolaan sumber daya air, perencanaan pertanian, serta strategi mitigasi banjir di Pulau Jawa.Kata Kunci: Iklim, Kriging; MAPE; Curah hujan; SAR-X. 2020MSC: 62H11, 86A32
Spatial Weight Matrix Comparison of SAR-X Model using Casetti Approach Almeira Tsanawafa; Dianne Amor Kusuma; Budi Nurani Ruchjana
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 1 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i1.25579

Abstract

The Spatial Autoregressive Exogenous (SAR-X) model with the Casetti approach is used to describe the influence of location and exogenous variables in the description and prediction of spatial observations, namely, people's habits and behavior towards culture in Java Island. The SAR-X model with the Casetti approach is characterized by a spatial weight matrix that describes the coordinates of the region at each location. The spatial weight matrix is determined outside the model. This study examines the spatial weight matrix determined based on rook contiguity, bishop contiguity, queen contiguity, inverse distance and inverse distance squared, and compares the application of the spatial weight matrix to the SAR-X model with the Casetti approach for the description and prediction of people's habits and behavior towards culture in Java Island. The description and prediction results obtained are measured using the Root Mean Square Error (RMSE) value. The results of data processing show that the best spatial weight matrix in the SAR-X model with the Casetti approach to community habits and behavior in Java Island is the inverse distance squared spatial weight matrix, supported by the calculation of the minimum RMSE value and the coefficient of determination above 60%.
SPATIAL INTERPOLATION OF RAINFALL INTENSITY IN JAVA ISLAND USING ORDINARY KRIGING Auliyazhafira, Shabira A.; Putri, Fariza A.; Nauli, Theresia S.; Al Madani, Aulia R.; Jaya, I Gede Nyoman Mindra; Falah, Annisa N.; Ruchjana, Budi Nurani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1791-1804

Abstract

Indonesia, situated between two continents and two oceans, experiences a complex climate system influenced by global warming. Climate change has disrupted weather patterns, making it increasingly difficult to predict the rainy and dry seasons and rainfall intensity. However, neighboring regions often exhibit similar weather characteristics, which can be leveraged for prediction. As Indonesia’s economic center, Java Island displays distinct yet interconnected weather patterns, making accurate rainfall prediction crucial for various sectors. This study utilizes 10 years of average rainfall data from NASA’s Power database, covering 64 observation points across Java. Ordinary point kriging is the estimation of a value at a given point and is often used in spatial interpolation analysis in general. Through ordinary point kriging analysis, this study aims to find an accurate kriging equation for predicting rainfall in various regions of Java Island. To achieve this, semivariogram modeling was performed to determine the best theoretical model for spatial interpolation. From 53 sampled regions, 1,378 sample pairs were used to calculate the experimental semivariogram obtained using the R programming language. Next, the theoretical semivariogram was determined using the sill parameter derived from the variance of the sampled data. Three theoretical semivariogram models were considered: spherical, exponential, and Gaussian. The results indicated that the exponential model was the most suitable as it had the smallest SSE value. The results of this analysis enrich our understanding of climate patterns in Indonesia and will contribute to developing mitigation and adaptation strategies related to climate change in the future. The Kriging equation obtained can provide highly accurate prediction results on the test data with a MAPE (Mean Absolute Percentage Error) error measure of 4.85% and RMSE (Root Mean Square Error) of 18.17, which indicates that the prediction results obtained are highly accurate predictions.
Canonical Correlation Analysis of Global Climate Elements and Rainfall in the West Java Regions Bowo, Arisya Maulina; Irianingsih, iin; Ruchjana, Budi Nurani
Desimal: Jurnal Matematika Vol. 3 No. 2 (2020): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v3i2.5870

Abstract

Indonesia has a diversity of climate influenced by several global phenomena such as El Nino Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), and Asian-Australian Monsoon. Continuously climate changing indirectly causes a hydrometeorological disaster. The purpose of this study was to analyze the relationship between global climate elements (ENSO, IOD, Asian-Australian Monsoon) with rainfall in the West Java regions (Bogor Regency, Bandung Regency, Sukabumi Regency, Garut Regency, and Kuningan Regency) simultaneously. The selection of the five regions was based on the natural disaster reports of Badan Nasional Penanggulangan Bencana (BNPB). The research method used was a quantitative research method through one of multivariate analysis technique called canonical correlation analysis. The results of this study indicate that there was a simultaneous relationship between global climate elements, with rainfall in the West Java regions by 0.819. The global climate element and rainfall in the West Java regions that most influenced the relationship were Asian-Austalian Monsoon and Kuningan Regency rainfall.
Rainfall Model Using Principal Component Regression Analysis with R Software in Sulawesi Yunia, Annisa Alma; Kusuma, Dianne Amor; Suhandi, Bambang; Ruchjana, Budi Nurani
Desimal: Jurnal Matematika Vol. 3 No. 3 (2020): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v3i3.6108

Abstract

Indonesia is a tropical country that has two seasons, rainy and dry. Nowadays, the earth is experiencing the climate change phenomenon which causes erratic rainfall. The rainfall is influenced by several factors, one of which is the local scale factor. This research was aimed to build a rainfall model in Sulawesi to find out how the rainfall relationship with local scale factor in Sulawesi. In this research, the data used were secondary data which consisted of 15 samples with 6 variables from Badan Pusat Statistik (BPS). The limitation of the sample size in this study was due to the limited secondary data available in the field. The data was processed using Principal Component Regression Analysis. The first step was reducing local scale factor variables so that the principal component variable could be obtained that can explain variability from the original data which then that variable was analyzed using principal regression analysis. The data were analyzed by utilizing R Studio software. The results show that two principal component variables can explain 75.2% of the variability of original data and only one principal component variable that was significant to the rainfall variable. The regression model explained that the relationship between rainfall, humidity, air temperature, air pressure, and solar radiation was in the same direction while the relationship between rainfall and wind velocity was not in the same direction. Overall, the results of the study provided an overview of the application of the Principal Component Regression analysis to model the rainfall phenomenon in the Sulawesi region using the R program.
Co-Authors Ahdian, Muhammad Rhafi Ahmad Fawaid Ridwan Akmaliah, Syifani Al Fataa W Haq Al Madani, Aulia R. Al Madani, Aulia Rahman Alawiyah, Mutik Almeira Tsanawafa Almeira Tsanawafa Anggraeni A Ani Pertiwi Annisa Alma Yunia Annisa Nur Falah, Annisa Nur Arisya Maulina Bowo Armalia Desiyanti Asep Kurnia Permadi Asep Kurnia Permadi Asri Yuniar Asrirawan Atika Tresna Arianto Atje Setiawan Abdullah Auliyazhafira, Shabira A. Ayu Indriani Ayun Sri Rahmani Bambang Suhandi Bambang Suhandi Bowo, Arisya Maulina Dedi Rosadi Delvi Rutania Prama Devi Munandar, Devi Devi Yanti Diah Chaerani Dian Islamiaty Puteri Dianne Amor Kusuma Dianne Amor Kusuma Dicky Muslim Dwipriyoko, Estiyan Eddy Hermawan Emah Suryamah Emah Suryamah, Emah Endang Rusyaman Endang Soeryana Hasbullah Fadhilah, Dila Nur Fajriatus Sholihah Falah, Annisa N. Gumgum Darmawan Gumgum Darmawan Hamim Tsalis Soblia Hardianto A Hendarmawan Hendarmawan Hendarmawan Hendarmawan, Hendarmawan Hera Khoirunnisa Husein Hernadi Bahti Husnul Chotimah I Gede Nyoman Mindra I Gede Nyoman Mindra Jaya I Gede Nyoman Mindra Jaya Ibrahim, Riza Andrian Iin Irianingsih Kankan Parmikanti Kartika Sari Khafsah Joebaedi Khoirunnisa Rohadatul Aisy Muslihin Khoirunnisa Rohadatul Aisy Muslihin Kusuma, Dianne Amor Lucy Fitria Dewi Mahrudinda Mahrudinda Maryanto Rompon Mindra, I Gede Nyoman Monika, Putri Muhamad Sobari Muhamad Sobari Muhammad Herlambang Prakasa Yudha Muthalib A nadhira, valda azka Nadira Annisafiya Najwa, Sandrina Nauli, Theresia S. Noverlina Putri Permatasari Novi - Saputri Nur Hamid NUR HAMID Nurdeni, Nurdeni Pandu Permana Pratiwi, Dhanti Aurilia Pratomo, Firdaus Ryan Puteri, Dian Islamiaty Putri Monika Putri Monika Putri Monika Putri, Fariza A. Putri, Salsabila Eka Resa Septiani Pontoh Rizka Pradita Prasetya Rizki Apriva Hidayana Salsabil, Tsuroyya Salsabila Salsabila Setialaksana, Wirawan - Shailla Rustiana Sobari, Muhamad Soetikno, Christophorus Sri Adi Widodo Sri Indra Maiyanti Suhandi, Bambang Sutawanir Darwis Tegar Bratasena WKM Tilas Notapiri Toni Toharudin Tsuroyya Salsabil Tubagus Robbi Megantara Viona Prisyella Balqis Vivian Wilhelmina Vivian Wilhelmina Wenny Srimeinda Tarigan WKM, Tegar Bratasena Yunia, Annisa Alma Zahra, Nabila Zulfa Hidayah Satria Putri