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Jurnal Fourier
Published by Universitas Islam Negeri Sunan Kalijaga Yogyakarta
ISSN : -     EISSN : -     DOI : -
Core Subject : Economy, Science, Education,
Computer Science & IT Economics, Econometrics & Finance Education Mathematics
FOURIER adalah Jurnal Ilmiah bidang yang memadukan dan mengembangkan ilmu Matematika dan pembelajarannya yang diintegrasikan dan interkoneksikan dengan nilai-nilai keislaman terbit sejak tahun 2012 dengan frekuensi terbit 2 kali dalam setahun yang dengan bahasa utama (Bahasa Indonesia dan Bahasa Inggris) yang proses reviewernya sesuai dengan disiplin ilmunya (Analisis, Aljabar, Matematika Terapan, Statistika, dan Pendidikan Matematika).
Arjuna Subject : -
Articles 192 Documents
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Peramalan Jumlah Penumpang Kereta Api Nasional dengan Model Hybrid ARIMAX-XGBoost Menggunakan Dummy Intervensi Rafi Kamindra; Dadan Dasari; Fitriani Agustina
Jurnal Fourier Vol. 15 No. 1 (2026)
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.2026.151.45-53

Abstract

Abstrak Keberadaan guncangan struktural (structural break) pada data deret waktu menyebabkan metode peramalan linear konvensional memiliki keterbatasan dalam menghasilkan akurasi yang tinggi. Keterbatasan ini sangat terlihat pada data mobilitas penumpang kereta api nasional yang merekam fluktuasi ekstrem dan perubahan level secara permanen akibat krisis makro di masa lalu, seperti pandemi COVID-19. Penelitian ini bertujuan membangun model peramalan yang adaptif menggunakan pendekatan Hybrid yang menggabungkan model statistik linear Autoregressive Integrated Moving Average with Exogenous Variables (ARIMAX) dan algoritma Machine Learning non-linear eXtreme Gradient Boosting (XGBoost). Metodologi dilakukan dalam dua tahap, yaitu estimasi komponen linear dan dampak kebijakan menggunakan ARIMAX dengan empat variabel dummy intervensi, dilanjutkan dengan pemodelan sisaan (residual) yang mengandung pola non-linear menggunakan XGBoost. Hasil analisis menunjukkan model linear terbaik adalah ARIMAX(0,1,3) dengan residu yang terbukti tidak berdistribusi normal, menjustifikasi penggunaan XGBoost pada tahap kedua. Evaluasi kinerja pada data uji (out-of-sample) membuktikan bahwa model Hybrid ARIMAX-XGBoost lebih unggul dibandingkan model ARIMAX tunggal, dengan penurunan nilai RMSE sebesar 2,76% dan perbaikan akurasi MAPE sebesar 2,81%, sehingga pendekatan ini lebih efektif digunakan untuk perencanaan operasional transportasi di era pemulihan pasca-pandemi. Abstract The existence of structural breaks in time series data causes conventional linear forecasting methods to have limitations in producing high accuracy. This limitation is highly evident in the national train passenger mobility data, which records extreme fluctuations and permanent level shifts due to past macro crises, such as the COVID-19 pandemic. This study aims to build an adaptive forecasting model using a Hybrid approach combining the linear statistical model Autoregressive Integrated Moving Average with Exogenous Variables (ARIMAX) and the non-linear Machine Learning algorithm eXtreme Gradient Boosting (XGBoost). The methodology was conducted in two stages, estimating linear components and policy impacts using ARIMAX with four intervention dummy variables, followed by modeling the residuals containing non-linear patterns using XGBoost. The analysis results indicated that the best linear model was ARIMAX(0,1,3) with residuals proven to be non-normally distributed, justifying the use of XGBoost in the second stage. Performance evaluation on testing data (out-of-sample) demonstrated that the Hybrid ARIMAX-XGBoost model outperformed the single ARIMAX model, with a 2.76% decrease in RMSE and a 2.81% improvement in MAPE accuracy, proving that this approach is more effective for transportation operational planning in the post-pandemic recovery era.
Prime Graph Over Semidihedral Group and Its Connectivity Indices Riyanto Riyanto; Arif Munandar
Jurnal Fourier Vol. 15 No. 1 (2026)
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.2026.151.54-62

Abstract

This study investigates the structural properties and topological connectivity indices of the prime graph associated with the semidihedral group of order 2 raised to the power of n, whose vertex set consists of all elements of the group. Two distinct vertices are adjacent precisely when the greatest common divisor of their orders is a prime number. Since the identity element has order one, it is not adjacent to any other vertex and therefore forms an isolated vertex. Consequently, the prime graph is disconnected and consists of the isolated identity element together with a non-trivial connected component containing all remaining group elements. The vertex set is partitioned into three disjoint subsets consisting of the identity element, elements of order two, and elements of order greater than two. Based on this partition, we characterize the degree sequence, diameter, radius, and clique number of the graph. Furthermore, exact closed-form analytical formulas are obtained for several fundamental degree-based and distance-based topological connectivity indices, including the First Zagreb index, Wiener index, Hyper-Wiener index, Harary index, and Forgotten index.

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