A Copula-Garch Modelcopula-Garch Model

摘要

In the present study we develop a new two-dimensional Copula-GARCH model. This type of two-dimensional process is characterized by a dependency structure modeled using a copula function. For the marginal densities we employ a GARCH(1,1) model with innovations drawn from a t-Student distribution. The model can be easily extended by using more sophisticated processes for the marginal densities. The static specification of the model assumes that the dependency structure of the two data series does not vary in time implying that the parameters of the copula function are constant. On the other hand, the dynamic specification models explicitly the dynamics of these parameters. We econometrically estimate the parameters of the two specifications using various copula functions, focusing on the mixture between the Gumbel and Clayton copulas. We employ daily index returns from two emerging and two developed financial markets. The main finding is that including a varying dependency structure improves the goodness-of-fit of the Copula-GARCH model.~(1)Sa?etakU ovom smo istra?ivanju razvili novi dvodimenzionalni Copula-GARCH model. Ovu vrstu dvodimenzionalnih procesa karakterizira zavisna struktura stvorena koriste?i spojnu funkciju (kopulu). Za marginalne gusto?e koristili smo GARCH(1,1) model s inovacijama preuzetim iz t-Student distribucije. Model se mo?e lako pro?iriti koriste?i sofisticiranije procese za marginalne gusto?e. Stati?ka specifikacija modela pretpostavlja da zavisna struktura dva niza podataka ne varira u vremenu te tako podrazumijeva da su parametri spojne funkcije konstantni. S druge strane, dinami?ka specifikacija eksplicitno odre?uje dinamiku ovih parametara. Ekonometrijski procjenjujemoparametre dvije specifikacije koriste?i razne spojne funkcije, uz naglasak na mje?avinu izme?u Gumbelove i Claytonove kopule. Koristili smo dnevne indekse zarade s dva razvijena i dva financijska tr?i?ta u razvoju. Glavni nalaz upu?uje na to da uklju?ivanje promjenjive zavisne strukture pobolj?ava sukladnost distribucije Copula-GARCH modela.