Multivariate elliptically contoured stable distributions with applications to BRICS financial data.

Abstract

Brazil, Russia, India, China and South Africa (BRICS) are regarded as the ve major emerging economies where all members are a part of a select group of developing industrialized countries. In the nancial industry, various models are used for the description and analysis of nancial trends. One of these models is the family of stable distributions which takes into account the skewness and heavy tails that are frequent in nancial data. The main objective of this study is to investigate the t of stable distributions for exchange rates of each of the BRICS countries against the U.S. Dollar in both the univariate and multivariate cases. The data set consists of exchange rate data from the period January 2011 to January 2016. Nolan's S0 -parameterization stable distribution was tted using the maximum likelihood method in the univariate case and in a tted stable model where a GARCH (1,1) lter was applied to the returns (Stable-GARCH(1,1)). The Kolmogorov-Smirnov test and the Anderson-Darling test show that stable distributions adequately t the returns of BRICS nancial data. Value-at-Risk (VaR) calculations and VaR in-sample backtesting using the Kupiec likelihood ratio test and the Christo ersen's conditional coverage test were applied as per the International Basel Regulatory where the robustness of each model describing the nancial data was evaluated. Thereafter, we proceeded to t bivariate elliptical stable models using the Rachev-Xin-Cheng method after visualizing the scatterplot matrix of BRICS countries. This study validates the usefulness of stable distributions for modelling BRICS nancial data.