MODEL VOLATILITAS GARCH(1,1) DENGAN ERROR STUDENT-T UNTUK KURS BELI EUR DAN JPY TERHADAP IDR
(1) Prodi Matematika, Fakultas Sains dan Matematika, Universitas Kristen Satya Wacana, Indonesia
(2) Prodi Matematika, Fakultas Sains dan Matematika, Universitas Kristen Satya Wacana, Indonesia
(3) Prodi Matematika, Fakultas Sains dan Matematika, Universitas Kristen Satya Wacana, Indonesia
Abstract
Studi ini menyajikan model volatilitas Generalized Autoregressive Conditional Heteroscedasticity (GARCH)(1,1) untuk returns keuangan yang mengasumsikan bahwa returns error berdistribusi Student-t. Parameter dari model volatilitas diestimasi menggunakan algoritma Markov Chain Monte Carlo (MCMC). Secara khusus, nilai-nilai parameter model dibangkitkan menggunakan metode adaptive random walk Metropolis dan independence chain Metropolis–Hasting (IC-MH) yang dikonstruksi dalam algoritma MCMC. Model dan metode diaplikasikan pada data kurs beli harian Yen Jepang (JPY) dan Euro (EUR) terhadap Rupiah Indonesia (IDR) pada periode Januari 2009 sampai dengan Desember 2014. Berdasarkan kriteria faktor Bayes, hasil empiris menunjukkan dukungan sangat kuat terhadap asumsi distribusi student-t untuk returns error.
This study investigates a volatility GARCH(1,1) model with Student’s t-error distribution for financial return. The parameters of GARCH model are estimated by using Markov Chain Monte Carlo (MCMC) algorithm. Specifically, the draws are sampled using adaptive random walk Metropolis and independence chain Metropolis–Hastings (IC-MH) methods that constructed in the MCMC algorithm. The model and methods are applied to the daily buying rate data of the Euro (EUR) and Japanese Yen (JPY) to Indonesian Rupiah (IDR) from January 2009 to December 2014. According to the Bayes factor criteria, empirical results shows a strong support to the assumption of Student’s t-error distribution.
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