Multivariate elliptically contoured stable distributions with applications to BRICS financial data.
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Date
2016
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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.
Description
Master of Science in Statistics. University of KwaZulu-Natal, Durban 2016.
Keywords
Theses - Statistics.