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All Journal Jurnal Sains dan Teknologi BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Limits: Journal of Mathematics and Its Applications Jurnal Sains dan Edukasi Sains Prosiding University Research Colloquium
Faldy Tita
Universitas Kristen Satya Wacana
Humanities Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Environmental Science Law, Crime, Criminology & Criminal Justice Materials Science & Nanotechnology Mathematics Mechanical Engineering Medicine & Pharmacology Physics Transportation Other

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Analisis Empiris dari Variasi Kontinu dan Lompatan dalam Model Threshold GARCH dengan Ukuran Realized Nugroho, Didit Budi; Hanafi, Fika Maula; Puspitasari, Agnes Dhika; Tita, Faldy; Larwuy, Lennox
Limits: Journal of Mathematics and Its Applications Vol 21, No 3 (2024)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v21i3.20426

Abstract

Volatilitas adalah ukuran fluktuasi harga aset keuangan yang tak terpisahkan dari dinamika pasar, tidak hanya sebagai indikator risiko tetapi juga sebagai sumber informasi tentang peluang dan ketidakpastian bagi investor. Pendekatan utama dalam mengukur risiko pasar keuangan yaitu dengan pemodelan dan estimasi volatilitas. Studi ini fokus pada pemodelan volatilitas menggunakan kerangka Threshold Generalized Autoregressive Conditional Heteroskedasticity (TGARCH). Pertama kali ini mengkonstruksi model TGARCH-X dan Realized TGARCH (RealTGARCH) yang memperhatikan ukuran Realized Volatility (RV) sebagai variabel eksogen. Selanjutnya, model tersebut dikembangkan menjadi model TGARCH-CJ dan RealTGARCH-CJ dengan cara mendekomposisi komponen RV menjadi komponen kontinu dan lompatan. Analisis empiris didasarkan pada hasil estimasi model menggunakan metode Adaptive Random Walk Metropolis untuk data Tokyo Stock Price Index (TOPIX) Jepang. Perbandingan pencocokan model menunjukkan keunggulan yang signifikan untuk model-model dengan komponen kontinu dan lompatan. Dengan pengaplikasian ukuran RV interval waktu 1 dan 5 menit, model terbaik diberikan oleh RealTGARCH-CJ yang mengadopsi ukuran RV 1 menit.
Improvement of Real-GJR Model using Jump Variables on High Frequency Data Nugroho, Didit Budi; Wulandari, Nadya Putri; Alfagustina, Yumita Cristin; Parhusip, Hanna Arini; Tita, Faldy; Susanto, Bambang
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.24294

Abstract

Volatility is a key indicator in assessing risk when making investment decisions. In the world of financial markets, volatility reflects the degree to which the value of a financial asset fluctuates over a given period. The most common way to measure the future loss potential of an investment is through volatility. Focusing on the Realized GJR (RealGJR) volatility model, which consists of return, conditional volatility, and measurement equations, this study proposes the RealGJR-CJ model developed by decomposing the exogenous variable in the volatility equation of RealGJR into continuous C and discontinuous (jump) J variables. The decomposition of exogenous variables makes the RealGJR-CJ model follow realistic financial markets, where the asset volatility is a continuous process with some jump components. As an empirical illustration, the models are applied to an index in the Japanese stock market, namely Tokyo Stock Price Index, covering from January 2004 to December 2011. The observed exogenous variable in the volatility equation of RealGJR models is Realized Volatility (RV), which is calculated using intraday data with time intervals of 1 and 5 minutes. Adaptive Random Walk Metropolis method was employed in Markov Chain Monte Carlo algorithm to estimate the model parameters by updating the parameters during sampling based on previous samples from the chain. From the results of running the MCMC algorithm 20 times, the mean of the information criteria of competing models is significantly different based on standard deviation and the result suggests that the model with continuous and jump variables can improve the model without jump. The best fit model is provided by RealGJR-CJ with the adoption of 1-minute RV data. 
Perbandingan Kinerja Metode Support Vector Regression dan Metode Regresi Linier Berganda dalam Memprediksi BMI pada Dataset ASTHMA Kurniawan, Titus Antonius David; Setiawan, Adi; Tita, Faldy
Jurnal Sains dan Edukasi Sains Vol. 8 No. 2 (2025): Jurnal Sains dan Edukasi Sains
Publisher : Faculty of Science and Mathematics, Universitas Kristen Satya Wacana, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24246/juses.v8i2p133-142

Abstract

Body Mass Index (BMI) merupakan metode untuk mengevaluasi apakah seseorang memiliki berat badan ideal, yang berperan penting dalam mengidentifikasi risiko kesehatan seperti penyakit jantung dan diabetes. Dalam penelitian ini, BMI digunakan sebagai variabel prediktor untuk menentukan kemungkinan seseorang menderita asma, yaitu penyakit kronis yang memengaruhi saluran pernapasan. Untuk memprediksi BMI berdasarkan variabel-variabel lain dalam dataset Asthma, penelitian ini membandingkan dua metode regresi, yaitu regresi linier berganda dan Support Vector Regression (SVR). Evaluasi akurasi model dilakukan menggunakan Mean Absolute Percentage Error (MAPE), yang mengukur kesalahan prediksi dalam bentuk persentase, di mana nilai MAPE yang lebih rendah menunjukkan tingkat akurasi prediksi yang lebih baik. Data uji dibagi menjadi empat skenario, yaitu 10%, 20%, 30%, dan 40% dari keseluruhan data. Hasil perhitungan menunjukkan bahwa metode regresi linier berganda menghasilkan nilai MAPE sebesar 15,42%; 15,44%; 15,51%; dan 15,63% secara berturut-turut. Sementara itu, metode SVR menghasilkan nilai MAPE sebesar 15,77%; 15,74%; 15,77%; dan 15,81%. Berdasarkan hasil tersebut, regresi linier berganda terbukti memberikan prediksi yang lebih akurat dibandingkan SVR dalam konteks dataset Asthma. Dengan demikian, regresi linier berganda lebih efektif dalam memodelkan BMI dibandingkan SVR dan dapat menjadi pertimbangan penting dalam pengembangan model prediktif untuk mendukung pengambilan keputusan terkait risiko penyakit pernapasan seperti asma.
CONSTRUCTION OF SUBSTITUTION BOX (S-BOX) BASED ON IRREDUCIBLE POLYNOMIALS ON GF(2^8) Tita, Faldy; Setiawan, Adi; Susanto, Bambang
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 1 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss1pp0517-0528

Abstract

In the field of modern encryption algorithms, the creation of S-Box is an essential element that plays an important role in maintaining data security in various industries. This article provides a comprehensive review of various S-Box designs, with particular emphasis on essential parameters such as “Average ”, “Average ” and “Non-linearity value”. The main goal is to determine the most optimal S-Box structure to minimize correlation, thereby improving the security and unpredictability of the cryptographic system. Research results indicate that the S-Box characterized by the 1BD hexadecimal code is superior to its counterparts. It has an average value of 4.1953 and an average value of 0.4756. In contrast, the S-Box represented by hexadecimal code 169 displays a relatively lower level of security, with an average d value of 3.8750 and an average value of 0.5156. These results enable security experts and cryptographers to make the correct choice when selecting the S-Box with the minimum correlation value, thereby strengthening cryptographic systems against emerging cyber threats.
S-BOX CONSTRUCTION IN THE ADVANCED ENCRYPTION STANDARD (AES) DEVELOPMENT ALGORITHM IN GF(2^2), GF(2^4) & GF(2^6) Setiawan, Adi; Tita, Faldy; Susanto, Bambang
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 4 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss4pp2329-2344

Abstract

This research aims to obtain a method for constructing S-boxes based on GF(22), GF(24) and GF(26). A review of the Galois Field GF(2m) is presented for m=1,2,3,4,5 and 6. Furthermore, it is used to construct an S-box based on GF(22), GF(24) and GF(26). Based on these results, later it can be developed for S-box construction in the AES algorithm which uses the Galois Field GF(2m) for m>=10.
The GARCH-X(1,1) Model with Exponentially Transformed Exogenous Variables Nugroho, Didit; Dimitrio, Obed; Tita, Faldy
JST (Jurnal Sains dan Teknologi) Vol. 12 No. 1 (2023): April
Publisher : Universitas Pendidikan Ganesha

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23887/jstundiksha.v12i1.50714

Abstract

Model Generalized Autoregressive Conditional Heteroskedasticity (GARCH) dengan mempertimbangkan efek dari variabel eksogen pada proses volatilitas, dinamakan GARCH-X(1,1), telah sukses memperbaiki pencocokan dan prediksi volatilitas dari model GARCH. Variabel eksogen yang sering digunakan adalah ukuran Realized Volatility (RV). Untuk mereduksi kemencengan dari RV sehingga mampu memperbaiki pencocokan model, studi ini mengaplikasikan transformasi eksponensial pada variabel eksogen dalam model GARCH-X(1,1). Tujuan tersebut dicapai melalui studi empiris berdasarkan pada data returns dan RV 10 menit (sebagai variabel eksogen) dari indeks harga saham FTSE100 dan SP500 periode harian dari Januari 2000 sampai Desember 2021 yang diambil dari Oxford-man Institute’s “Realized Library”. Analisis didasarkan pada hasil estimasi model dengan error dari returns berdistribusi Normal dan Student-t menggunakan Metode Adaptive Random Walk Metropolis diimplementasikan dalam algoritma Markov Chain Monte Carlo. Interval High Posterior Density pada tingkat kepercayaan 99% mengindikasikan signifikansi dari transformasi eksponensial untuk variabel eksogen pada kedua kasus asumsi distribusi untuk error dari returns. Terlebih lagi, nilai Akaike Information Criterion (AIC) mengindikasikan bahwa model yang diusulkan menggungguli model dasar GARCH-X(1,1), dimana model pencocokan terbaik diberikan oleh model berdistribusi Student-t.
Study on The Continuous-Jump Behavior of Asset Return Volatility Through The GJR Model Alfagustina, Yumita Cristin; Nugroho, Didit Budi; Tita, Faldy
Prosiding University Research Colloquium Proceeding of The 17th University Research Colloquium 2023: Bidang MIPA dan Kesehatan
Publisher : Konsorsium Lembaga Penelitian dan Pengabdian kepada Masyarakat Perguruan Tinggi Muhammadiyah 'Aisyiyah (PTMA) Koordinator Wilayah Jawa Tengah - DIY

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

Abstract

Generalized Auto-Regressive Conditional Heteroskeasticity (GARCH) is a model used to predict the volatility of returns. Volatility is a statistical measure of the movement of returns for securities (financial instruments that can only be traded through markets or securities companies) or certain market indices. Then the GARCH model was further developed into an asymmetric form, namely conditional volatility and returns have a relationship, namely the GJR model which is an abbreviation of the name (Glosten- Jagannathan-Runkle). This research focuses on the GJR-X by adding high-frequency exogenous variables in volatility process and on the GARCH-CJ which is a decomposition of the exogenous variable X, namely the continuous component C (Continuous) and the jump J (Jump). TOPIX data (Tokyo Stock Price Index) is the real data used in this study. To estimate the model parameters, the ARWM (Adaptive Random Walk Metropolis) method will be used with the MCMC (Markov Chain Monte Carlo) algorithm. First, it was found that the ARWM method is good at estimating parameters. Second, the AIC value of GJR-CJ was smaller than that of GJR-X, which means that GJR-CJ had better data fitting.
Co-Authors Adi Setiawan Alfagustina, Yumita Cristin Bambang Susanto Didit Budi Nugroho Didit Nugroho, Didit Dimitrio, Obed Hanafi, Fika Maula Hanna Arini Parhusip Kurniawan, Titus Antonius David Lennox Larwuy Puspitasari, Agnes Dhika Wulandari, Nadya Putri