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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan InPrime: Indonesian Journal Of Pure And Applied Mathematics Innovative: Journal Of Social Science Research
Najwa, Sandrina
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Humanities Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Law, Crime, Criminology & Criminal Justice Mathematics Mechanical Engineering Physics Public Health Transportation Other

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Model Peramalan Double Seasonal Pada Data Konsumsi Gas Alam Amerika Serikat Dengan Pendekatan Analisis Spektral Fitriani Azuri, Dila; Putri Syallya, Najma Rafifah; Najwa, Sandrina; Alifia, Wanda; Darmawan , Gumgum
Innovative: Journal Of Social Science Research Vol. 3 No. 6 (2023): Innovative: Journal Of Social Science Research
Publisher : Universitas Pahlawan Tuanku Tambusai

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Gas alam merupakan sumber energi utama di seluruh dunia dan saat ini banyak digunakan untuk berbagai keperluan di Amerika Serikat. Konsumsi gas alam di Amerika Serikat memiliki pola double seasonal yang terjadi karena faktor iklim. Tujuan dari penelitian ini adalah untuk menemukan periode tersembunyi pada data dan meramalkan konsumsi gas alam dengan menggunakan analisis spektral dan metode Double Seasonal ARIMA. Hasil analisis spektral menunjukkan bahwa terdapat double seasonal dengan periode 12 bulan dan 6 bulan, yang berarti karakteristik perubahan konsumsi gas alam di Amerika Serikat cenderung meningkat atau menurun setiap 12 bulan dan 6 bulan. Model yang terpilih, SARIMA(0,1,0)(1,1,4)6(1,1,1)12, menunjukkan keefektifannya dalam memprediksi pola konsumsi di masa mendatang dengan MAPE sebesar 2,61% yang mengindikasikan keandalan model yang tinggi.
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
APPLICATION OF THE PRINCIPAL COMPONENT ANALYSIS-VECTOR AUTOREGRESSIVE INTEGRATED (PCA-VARI) MODEL TO FORECASTING ECONOMIC GROWTH IN INDONESIA Al Madani, Aulia Rahman; Najwa, Sandrina; Ruchjana, Budi Nurani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2301-2316

Abstract

Indonesia's economic growth has undergone significant fluctuations in recent years, driven by global shocks such as the 2020 COVID-19 pandemic, the 2013 taper tantrum, and the 2022 global energy crisis. These events underscore the urgent need for more accurate and robust forecasting models to support economic stability and policymaking. This study applies the Principal Component Analysis-Vector Autoregressive Integrated (PCA-VARI) model to forecast economic growth in Indonesia. PCA reduces seven economic variables into two principal components for ten years (2012-2022). The results show that the first component (PC1) shows the highest correlation with the variables of Money Supply, BI Rate, and Foreign Exchange Reserves, which reflect monetary policy and financial stability. Meanwhile, the second component (PC2) is highly correlated to the GDP Index, Exchange Rate, and Inflation variables, which reflect macroeconomic conditions. VARI, as a non-stationary multivariate time series model, is used to model the relationship between these components, with the third-order lag selected as the optimal lag based on the Akaike Information Criterion (AIC), Hannan-Quinn Criterion (HQ), and Final Prediction Error (FPE) values. The results show that the PCA-VARI(3) model is able to provide highly accurate forecasting with a MAPE of 1.21% for PC1 and 1.34% for PC2, and has met all the necessary model assumptions.
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; rainfall; MAPE; SAR-X; SAR-X Kriging. 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: curah hujan; iklim; MAPE; SAR-X; SAR-X Kriging. 2020MSC: 62H11, 86A32
Co-Authors Ahdian, Muhammad Rhafi Al Madani, Aulia Rahman Alifia, Wanda Annisa Nur Falah, Annisa Nur Ayu Indriani Budi Nurani Ruchjana Darmawan , Gumgum Fitriani Azuri, Dila Mindra, I Gede Nyoman Pratiwi, Dhanti Aurilia Putri Syallya, Najma Rafifah