DEPENDENCE MODEL USING GRAPHICAL STRUCTURE THROUGH VINE COPULA AND ITS APPLICATION TO PREDICTION OF RISK MEASURE OF AGGREGATE OF RETURNS FOLLOWING GARCH PROCESS

• Main Author: Rahman Hakim, Arief
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/46673
• Institution: Institut Teknologi Bandung

Dependence model for paired data is a model which consists of a number of paired random variables. The dependence structure and measure of the paired data and their marginal distributions need to be considered in order to obtain the appropriate dependence model. For two-dimensional paired data, the simplest dependence model which can be chosen is the paired random variables with a certain standard joint distribution, such as bivariate normal or bivariate Student's t. If the dependence structure does not match, or the marginal distributions are from dierent distribution families, bivariate Copula can be used as an alternative to obtain more choices of the joint distribution. If the given paired data have three (or higher) dimensions, the choices of the standard joint distribution are increasingly limited. In this situation, a Copula which is constructed from bivariate Copulas using the pair-Copula construction method can be used. Their dependence model can be represented through Vine Copula using the graphical structure of R-Vine. This Vine Copula is applied to determine the dependence structure and joint distribution of three GARCH models for the returns of investment in three virtual currencies: Bitcoin, Ethereum, and Litecoin. The analysis is based on the data of daily closing price of those virtual currencies from January 1, 2017 to December 31, 2018. Then, Value-at-Risk predictions of each return and the aggregate are determined. Based on the estimated coverage probabilities, the computation which is made by involving the dependence structure of the GARCH models through Vine Copula yields fairly accurate predictions.