MODEL VOLATILITAS ARCH(1) DENGAN RETURN ERROR BERDISTRIBUSI SKEWED STUDENT-T

E. D. Saputri(1), D. B. Nugroho(2), A. Setiawan(3),

DOI: https://doi.org/10.15294/ijmns.v39i1.7707


(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

Model volatilitas Autoregressive Conditional Heteroscedasticity (ARCH)lag 1, dimana return error berdistribusi skewed Student-t, diaplikasikan untuk runtun waktu return kurs beli harian Euro (EUR) dan Japanese Yen (JPY) terhadap Indonesian Rupiah (IDR) dari Januari 2009 sampai Desember 2014. Metode indepence chain Metropolis-Hastings (IC-MH) yang efisien dibangun dalam algoritmaMarkov Chain Monte Carlo (MCMC) untuk memperbarui nilai-nilai parameter dalam model yang tidak bisa dibangkitkan secara langsung dari distribusi posterior. Meskipun 95% interval highest posterior density dari parameter skewness memuat nol untuk semua data pengamatan, tetapi sebagian besar distribusi posteriornya berada di daerah negatif, yang mengindikasikan dukungan terhadap distribusiskewed Student-t. Selain itu diperoleh nilai derajat kebebasan disekitar 15 dan 18, yang mengindikasikan dukungan terhadap heavy-tailedness.

Autoregressive Conditional Heteroscedasticity (ARCH) volatility model of lag 1, where return error has a skewed Student-t distribution,  for the buying rate Euro (EUR) and Japanese Yen (JPY) to Indonesian Rupiah (IDR) from January 2009 to December 2014,. An efficient independence chain Metropolis-Hastings (IC-MH) method is developed in an algorithm Markov Chain Monte Carlo (MCMC) to update the parameters of the model that could not be sampled directly from their posterior distributions. Although 95% highest posterior density interval from skewness parameter contains zero for all the data, most of the posterior distribution located in the negative area, indicating support for the skewed Student-t distribution into the return error. Furthermore the value of degrees of freedom is found around 15 and 18, indicating support for the heavy-tailedness.


Keywords

distribusi skewed Student-t, independence-chain Metropolis–Hastings, kurs beli, MCMC, model ARCH

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