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All Journal JTAM (Jurnal Teori dan Aplikasi Matematika) Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajarannya
Kholil, Zaini
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Education Mathematics

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Perbandingan Empiris antara Model Log-Garch dan Garch Kholil, Zaini; Nugroho, Didit Budi; Susanto, Bambang
Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajarannya 2019: Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajarannya
Publisher : Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (669.819 KB)

Abstract

Studi ini berfokus pada studi empiris tentang perbandingan antar model Log-GARCH(1,1) dan model GARCH(1,1). Kedua model diaplikasikan pada data simulasi dan data riil, data rill yang digunakan berjumlah tiga jenis data yaitu indeks harga saham Dow Jones Industrial Average (DJIA), Standard and Poor’s (S&P 500), dan S&P CNX Nifty pada periode harian dari bulan Januari tahun 2000 sampai bulan Desember tahun 2017. Model diasumsikan mempunyai inovasi return dengan berdistribusi normal. Solver Excel digunakan untuk mengestimasi model Log-GARCH(1,1) dan model GARCH(1,1) dan diselidiki kemampuannya. Secara keseluruhan, studi ini menunjukkan bahwa Solver pada Microsoft Excel mampu mengestimasi parameter-parameter model dengan cukup akurat. Dalam kasus data simulasi, hasil dari perhitungan nilai estimasi total log-likelihood mengindikasikan bahwa model Log-GARCH(1,1) berpotensi mencocokkan lebih baik dibandingkan dengn model GARCH(1,1). Sementara itu, dalam kasus data riil, hasil perhitungan nilai estimasi pada model GARCH(1,1) lebih cocok digunakan untuk ketiga data return harian indeks harga saham dibandingkan dengan model Log-GARCH(1,1).
GRG Non-Linear and ARWM Methods for Estimating the GARCH-M, GJR, and log-GARCH Models Nugroho, Didit Budi; Panjaitan, Lam Peter; Kurniawati, Dini; Kholil, Zaini; Susanto, Bambang; Sasongko, Leopoldus Ricky
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 2 (2022): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i2.7694

Abstract

Numerous variants of the basic Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have been proposed to provide good volatility estimating and forecasting. Most of the study does not work Excel’s Solver to estimate GARCH-type models. The first purpose of this study is to provide the capability analyze of the GRG non-linear method built in Excel’s Solver to estimate the GARCH models in comparison to the adaptive random walk Metropolis method in Matlab by own codes. The second contribution of this study is to evaluate some characteristics and performance of the GARCH-M(1,1), GJR(1,1), and log-GARCH(1,1) models with Normal and Student-t error distributions that fitted to financial data. Empirical analyze is based on the application of models and methods to the DJIA, S&P500, and S&P CNX Nifty stock indices. The first empirical result showed that Excel’s Solver’s Generalized Reduced Gradient (GRG) non-linear method has capability to estimate the econometric models. Second, the GJR(1,1) models provide the best fitting, followed by the GARCH-M(1,1), GARCH(1,1), and log-GARCH(1,1) models. This study concludes that Excel’s Solver’s GRG non-linear can be recommended to the practitioners that do not have enough knowledge in the programming language in order to estimate the econometrics models. It also suggests to incorporate a risk premium in the return equation and an asymmetric effect in the variance equation. 
Co-Authors Bambang Susanto Didit Budi Nugroho Dini Kurniawati Leopoldus Ricky Sasongko Panjaitan, Lam Peter