Dependence structure analysis with copula GARCH method and for data set suitable copula selection

Abstract

Objective: Multivariate GARCH (MGARCH) models are forecasted under normality. In this study, for non-elliptically distributed the data set which are generated Weilbull distribution. Copula-based GARCH (Copula-GARCH) was used. The aim of the paper is to model GARCH for non-normal distributions using copulas. Material and Methods: A two-step Copula-GARCH model to analyze the dependence structure of data sets was used. In the first step, we show data using univariate GARCH model to get standard residuals and construct marginal distributions. In this section GARCH (p,q) and GARCH (1,1) method are introduced. GARCH (1,1) method for data set was used for first step. In the second step, for dependence structures of the data sets were calculated Kendall Tau and Spearman Rho values which are nonparametric. Based on this method, parameters of copula are obtained. Results: A clear advantage of the copula-based model is that it allows for maximum-likelihood estimation using all available data. Conclusion: The aim of the method is basic to find the parameters that make the likelihood functions get its maximum value. With the help of the maximum-likelihood estimation method, for copula families obtain likelihood values. This values, Akaike information criteria (AIC) and Schwartz information criteria (SIC) are used to determine which copula supplies to suitability to the data set.