Skew Student-t Distribution
|
SfePCOMP |
NASCOMP |
JAPA500 |
MSACWFL | |
|
Location |
0.0062 |
0.0096 |
0.0013 |
0.0055 |
|
Scale |
0.0222 |
0.0357 |
0.0300 |
0.0196 |
|
Skewness |
0.8664 |
0.8506 |
0.9593 |
0.8593 |
|
Kurtosis |
5.4329 |
3.4153 |
4.5528 |
4.8423 |
|
LogLik |
2.fl79 |
2.0313 |
2.Ц60 |
2.5503 |
Skew Generalized Secant Hyperbolic Distribution
|
SfePCOMP |
NASCOMP |
JAPA500 |
MSACWFL | |
|
Location |
0.0061 |
0.0010 |
0.0011 |
0.0055 |
|
Scale |
0.0220 |
0.0334 |
0.0294 |
0.0193 |
|
Skewness |
0.8738 |
0.8440 |
0.9645 |
0.8599 |
|
Kurtosis |
-1.4014 |
-2.1752 |
-1.7483 |
-1.6308 |
|
LogLik |
2.fl60 |
2.0360 |
2.Ц77 |
2.5 f97 |
Skew Exponential Power Distribution
|
SfePCOMP |
NASCOMP |
JAPA500 |
MSACWFL | |
|
Location |
0.0065 |
0.0105 |
0.0020 |
0.0056 |
|
Scale |
0.0221 |
0.0330 |
0.0292 |
0.0193 |
|
Skewness |
0.8673 |
0.8416 |
0.9479 |
0.8571 |
|
Kurtosis |
0.6278 |
0.5358 |
0.6151 |
0.6166 |
|
LogLik |
24135 |
2.0332 |
2.1Ц6 |
2.5 f 67 |
5 Conclusions
In this paper we have studied the family of multivariate distributions by Koheler and
Smanowski in order to model financial returns and measure dependent risks. Fitting
the distribution to the returns of four market indices, the SfeP 500 Composite index
(SfePCOMP), the NASDAQ Composite index (NASCOMP), the NIKKEI 500 index
(JAPA500) and the MSCI AC World index (MSACWFL), with skewed Student t, gen-
eralized secant hyperbolic and generalized exponential power marginals, we have seen
that this distribution succeeds in properly interpreting the dependence structure of
data, apart from the marginals, introducing therefore some measures which can couple
the usual correlation indices in the interpretation of the strength of the link among
dependent risks. However, other important aspects of the distribution must be stud-
ied, for example the analysis of sensitivity of the parameters in presence of dependence
structures of higher order introduced by Koeheler and Symanovski (1995).
References
Ayebo, A. and Kozubowski, T.J. (2003): An Asymmetric Generalization of Gaus-
sian and Laplace Laws, Journal of Probability and Statistical Science, 1(2), 187—
210.
Caputo, A. (1998): Some Properties of the Family OfKoehler-Symanowski distribu-
tions. The Collaborative Research Center (SBF) 386, Discussion Paper No. 103,
University of Munich.
10
More intriguing information
1. Commitment devices, opportunity windows, and institution building in Central Asia2. Review of “From Political Economy to Economics: Method, the Social and Historical Evolution of Economic Theory”
3. Aktive Klienten - Aktive Politik? (Wie) Läßt sich dauerhafte Unabhängigkeit von Sozialhilfe erreichen? Ein Literaturbericht
4. APPLICATIONS OF DUALITY THEORY TO AGRICULTURE
5. The name is absent
6. Evolving robust and specialized car racing skills
7. Performance - Complexity Comparison of Receivers for a LTE MIMO–OFDM System
8. Keynesian Dynamics and the Wage-Price Spiral:Estimating a Baseline Disequilibrium Approach
9. Lumpy Investment, Sectoral Propagation, and Business Cycles
10. The Impact of Hosting a Major Sport Event on the South African Economy