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Study of Spatial Autoregressive Regression With Heteroskedasticity Using the Generalized Method of Moments and Bayesian Approach : Kajian Regresi Spasial Autoregresif dengan Heteroskedastik Menggunakan Generalized Method of Moments dan Pendekatan Bayes Koesnandy H, Abialam; Agus Mohamad Soleh; Farit Mochamad Afendi
Indonesian Journal of Statistics and Applications Vol 8 No 1 (2024)
Publisher : Statistics and Data Science Program Study, IPB University, IPB University, in collaboration with the Forum Pendidikan Tinggi Statistika Indonesia (FORSTAT) and the Ikatan Statistisi Indonesia (ISI)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/ijsa.v8i1p58-69

Abstract

Spatial dependence and spatial heteroskedasticity are problems in spatial regression. Spatial autoregressive regression (SAR) concerns only to the dependence on lag. The estimation of SAR parameters containing heteroskedasticity using the maximum likelihood estimation (MLE) method provides biased and inconsistent estimators. The alternative method that can be used are generalized method of moments (GMM) and Bayesian method. GMM uses a combination of linear and quadratic moment functions simultaneously so that the computation is easier than MLE. Bayesian method solves heteroskedasticity by modeling the structure of variance-covariance matrix. The bias are used to evaluate the GMM and Bayes in estimating parameters of SAR model with heteroskedasticity disturbances in simulation data. The results show that GMM and Bayes provides the bias of parameter estimates relatively consistent and smaller with larger number of observations. GMM and Bayes methods are applied to district/city GRDP data in Indonesia. The result show GMM method with Eksponential Distance Weights (EDW) matrix produces the minimum variance and the largest pseudo-R2
Comparison of ARIMA and GRU Models for High-Frequency Time Series Forecasting. Ridwan, Mochamad; Sadik, Kusman; Afendi, Farit Mochamad
Scientific Journal of Informatics Vol 10, No 3 (2023): August 2023
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/sji.v10i3.45965

Abstract

Purpose: The purpose of this research is to assess the efficacy of ARIMA and GRU models in forecasting high-frequency stock price data, specifically minute-level stock data from HIMBARA banks. In time series analysis, time series data exhibit interesting interdependence among observations. Despite its popularity in time series forecasting, the ARIMA model has limitations in capturing complicated nonlinear patterns. Forecasting high-frequency data is becoming more popular as technology advances and more high-frequency data becomes available.Methods: In this study, we compare the ARIMA and GRU models in forecasting minute-level stock prices of HIMBARA banks. The data used consists of 62,921 minute-level stock data points for each bank in the HIMBARA group, collected in the year 2022. The GRU model was chosen because it is capable of capturing complex nonlinear patterns in time series data. Each method's predicting performance is assessed using the Mean Absolute Percentage Error (MAPE) statistic.Results: In terms of forecasting accuracy, the GRU model outperforms the ARIMA model. The GRU model achieves a MAPE of 0.77% for BMRI stock, while the ARIMA model achieves a MAPE of 4.09%. The GRU model predicts a MAPE of 0.34% for BBRI stock, while the ARIMA model predicts a MAPE of 3.02%. For BBNI stock, the GRU model obtains a MAPE of 0.63%, while the ARIMA model achieves a MAPE of 1.52%. The GRU model achieves a MAPE of 0.58% for BBTN stock, while the ARIMA model achieves a MAPE of 6.2%.Novelty: In terms of minute-level time series data modeling, research in Indonesia has been limited. This study adds a new perspective to the discussion by comparing two modeling approaches: the traditional ARIMA model and the sophisticated deep learning GRU model, both of which are applied to high-frequency data. Beyond the present scope, there are several promising future directions to pursue, such as anticipating intraday stock fluctuations. This unexplored zone not only contributes to the field of financial modeling but also has the ability to uncover intricate patterns in minute-level data, an area that has not been extensively studied in the Indonesian context.
COMPARATIVE ANALYSIS OF BCBIMAX AND PLAID BICLUSTERING ALGORITHM FOR PATTERN RECOGNITION IN INDONESIA FOOD SECURITY Sumertajaya, I Made; Hikmah, Nur; Afendi, Farit Mochamad
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0335-0346

Abstract

Biclustering is an unsupervised learning algorithm that simultaneously groups rows and columns in a data matrix. Unlike conventional clustering, which evaluates objects across all variables independently, biclustering identifies subsets of objects and variables that share similar patterns—revealing localized structures within complex datasets. This study applies the BCBimax and Plaid algorithms to examine food security patterns across 34 Indonesian provinces. The indicators cover three key dimensions: availability, accessibility, and utilization of food. The algorithms are evaluated using the Jaccard Index, Mean Squared Residue (MSR), and the number of provinces effectively clustered. Results show that BCBimax, using a binarization threshold based on the median value, generates eight biclusters covering 58.8% of provinces. Meanwhile, the Plaid algorithm, applying constant column model parameters, produces six biclusters with 55.88% coverage, including overlapping memberships. Overall, BCBimax demonstrates superior performance, as indicated by a lower average MSR value (0.035) compared to Plaid (0.209). The Jaccard Index similarity score of 14.61% suggests that the biclusters formed by each method are significantly distinct. Both approaches indicate that the majority of Indonesian regions exhibit low to moderate food security characteristics.
PERFORMANCE EVALUATION OF SEASONAL ARIMA-SVR AND SEASONAL ARIMAX-SVR HYBRID METHODS ON FORECASTING PADDY PRODUCTION Risnawati, I'lmisukma; Afendi, Farit Mochamad; Sumertajaya, I Made
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0367-0380

Abstract

This study explores advances in forecasting time series data by combining linear and non-linear models. Traditional methods such as ARIMA and its variant ARIMAX are effective for linear data but have limitations when dealing with non-linearity. Support Vector Regression (SVR), a non-linear method, complements these weaknesses. Hybrid models such as ARIMA-SVR and ARIMAX-SVR synergize ARIMA or ARIMAX for linear components and SVR for non-linear components, improving accuracy. The purpose of this study is to evaluate the performance of hybrid ARIMA-SVR and ARIMAX-SVR methods on Indonesian paddy production data. The data analyzed is national-level data per sub-round (i.e., three sub-rounds per year) from sub-round 1 (January-April) of 1992 to sub-round 3 (September-December) of 2024, obtained from the Indonesian Central Statistics Agency and the Indonesian Ministry of Agriculture.Forecasting accuracy is measured using Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). The results show that the best model is the Seasonal ARIMAX (1,1,1)(0,1,1)[3]-SVR ( 0.05) hybrid model, with the smallest RMSE and MAPE values of 0.304 and 1.473%. The addition of the harvested area variable and the ASF dummy improved the accuracy of the ARIMAX model prediction, while the application of SVR to ARIMAX residuals successfully captured previously undetected linear patterns. Based on these considerations, the Seasonal ARIMAX(1,1,1)(0,1,1)[3]-SVR ( 0.05) hybrid model was selected as the model with the best performance.
Dimensionality Reduction Evaluation of Multivariate Time Series of Consumer Price Index in Indonesia Valentika, Nina; Sumertajaya, I Made; Wigena, Aji Hamim; Afendi, Farit Mochamad
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34151

Abstract

Multivariate time series (MTS) analysis of the Consumer Price Index (CPI) in Indonesia often encounters challenges such as outliers, missing data, and inter-variable correlations. Principal Component Analysis (PCA) is a practical approach for dimensionality reduction; however, its performance may vary depending on the data characteristics. This study is a quantitative comparative study that integrates empirical analysis and Monte Carlo simulation based on a first-order Vector Autoregressive (VAR(1)) model to evaluate three PCA approaches: Classical PCA, Robust PCA (RPCA), and PCA of MTS. These methods were applied to weekly price data of eight strategic food commodities across 70 districts and cities in Indonesia. The evaluation employed three criteria: (1) dimensionality reduction efficiency (empirical and simulation), (2) reconstruction accuracy measured using Root Mean Square Error (RMSE) (empirical), and (3) robustness to outliers and inter-variable correlations (simulation). Empirical results indicate that Classical PCA (lag 1) and RPCA (lag 1) are both efficient and effective in reducing dimensionality with minimal information loss. Using the first three principal components, all three methods were able to explain at least 85% of the total variance, with lag 1 identified as optimal. Simulation results reveal that RPCA (lag 1) provides the most stable and consistent performance in the presence of outliers, while Classical PCA (lag 2) performs better under conditions of high inter-variable correlation and a low proportion of outliers. These findings suggest that robust covariance estimation can improve the accuracy of dimensionality reduction and enhance the stability of multivariate time-series analysis for food price data in Indonesia.
Perbandingan Metode GARCH, LSTM, GRU, dan CNN pada Peramalan Volatilitas Kurs Adeline Vinda Septiani; Farit Mochamad Afendi; Anang Kurnia
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 1 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 1 Edisi Ma
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i1.3384

Abstract

Currency volatility is an important aspect of time series data analysis in economics and finance. This study aims to compare the performance of four methods: Generalized Autoregressive Conditional Heteroscedasticity (GARCH), Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Convolutional Neural Network (CNN), in predicting the volatility of the Rupiah against the US Dollar. The data used is daily exchange rates from January 2015 to March 2024. The evaluation is conducted by calculating the Root Mean Square Error (RMSE) and the percentage of actual values within a 95% confidence interval on training and testing data. The results indicate that LSTM achieves the lowest RMSE, with values of 5.30E-05 on training data and 2.50E-05 on testing data, demonstrating high accuracy in capturing non-linear patterns and long-term fluctuations. GRU records the highest percentage of actual values within the confidence interval, at 90.32% for training data and 91.72% for testing data, reflecting superior consistency compared to other methods. Meanwhile, GARCH shows competitive performance but lacks robustness on testing data. CNN exhibits the lowest performance, with high RMSE and a low percentage of data within the confidence interval. Overall, GRU emerges as the best method, offering an optimal balance between predictive accuracy and consistency, making it a reliable tool for modeling exchange rate volatility in high-volatility scenarios. Consequently, GRU is utilized for forecasting exchange rate volatility for the next 30 days. These findings contribute to the selection of appropriate methods for modeling exchange rate volatility, particularly amidst global market uncertainty.
Co-Authors . Indahwati . Sutoro Aam Alamudi Abd. Rasyid Syamsuri Adeline Vinda Septiani Agus Mohamad Soleh Agus Santoso Aji Hamim Wigena Akbar Rizki Akbar Rizki Akbar Rizki Aki Hirai Anang Kurnia Anggraini Sukmawati Annisa Malik Apino, Ezi Aqmar, Nurzatil Bagus Sartono Budi Susetyo Budi Waryanto Budi Waryanto Budi Waryanto Cici Suhaeni Dairul Fuhron Dalimunthe, Amir Abduljabbar Dian Ayuningtyas Eka Setiawaty Erwandi Erwandi fatimah Fatimah Febie Tri Lestari Fitrianto, Anwar H S, Rahmat Handayani, Vitri Aprilla Handayani, Vitri Aprilla Hari Wijayanto Hari Wijayanto Hasibuan, Rafika Aufa Hasnita Hasnita Herdina Kuswari Heri Retnawati Hiroki Takahashi I Made Sumertajaya Ikhlasul Amalia Rahmi Indahwati Indahwati Indahwati Isnan Mulia Itasia Dina Sulvianti Izzati, Fatkhul Kensuke Nakamura Khairil Anwar Notodiputro Koesnandy H, Abialam Kusman Sadik Latifah Kosim Darusman M. Rafi Maya Deanti Maysarah Sabariah Kudadiri Md. Altaf-Ul-Amin . Melati Mochamad Ridwan Mochamad Ridwan, Mochamad Mohammad Masjkur Muchlishah Rosyadah Muhammad Ali Umar Mukhamad Najib Nadhif Nursyahban Nur Hikmah Nur Janah Nur Jannah Nurul Qomariasih Octaviani, Siti Nurfajar Panjaitan, Intan Juliana Pardede, Timbul Pika Silvianti Pika Silvianti Pika Silvianti Puspita, Novi Qomariasih, Nurul Rifqi Aulya Rahman Risnawati, I'lmisukma Rizal Bakri Rossi Azmatul Barro Rosyada, Munaya Nikma Rosyadah, Muchlishah Rudi Heryanto Safitri, Wa Ode Rahmalia Septaningsih, Dewi Anggraini Septanti Kusuma Dwi Arini Shigehiko Kanaya Sulistiyani . Syahrir, Nur Hilal A. Syahrir, Nur Hilal A. Usman, Muhammad Syafiuddin Valentika, Nina Widhiyanti Nugraheni Widya Putri Nurmawati Winata, Hilma Mutiara Wisnu Ananta Kusuma Zana Aprillia