Statistic Panel A : [Y.sub.t] Mean 3.7957 Standard deviation 0.4370 Skewness -0.1045 Excess kurtosis
-1.4564 Minimum 3.1268 Maximum 4.7173 Jarque-Bera 113.2*** Statistic Panel B : [DELTA][Y.sub.t] Mean 0.0011 Standard deviation 0.0314 Skewness 7.4655 Excess kurtosis
155.9618 Minimum -0.1788 Maximum 0.6602 Jarque-Bera 1283600*** *** Indicates significance at 1% level.
This implies that if [c.sub.1] up to [c.sub.4] are equal to 0 then the distribution has zero skewness and excess kurtosis
; hence, this shows how to construct an infinite number of distributions that share this property with the normal.
Deviation 0.01659 Skewness -0.9885 Kurtosis 21.30 Excess Kurtosis
18.30 Jarque-Bcra 72,662 ** LB(Q) Test 22.43 ** ARCH Test 729.93 (p-value) (0.000) The Jarque-Bera test for normality distributed as Chi-square with 2[degrees] of freedom.
Kurt stands for the excess kurtosis
, and [[omega].sub.1] and [[omega].sub.2] are the optimal weights.
Recent studies, Gupta and Liang (2005), Dzikevicius (2005) and Patton (2009) show that the distribution of firm's returns risk is non-normal, with characteristics such as fat tails, excess kurtosis
, and skewness or heteroscedasticity.
(2002, 2003) demonstrate that distributions of hedge funds returns have a negative skewness and an excess kurtosis
. This leads to conclude that, for this type of fund, the challenge lies not only in the first two moments but also in higher moments.
The normal distribution has an excess kurtosis
of 0 but the distribution of home runs has an excess kurtosis
The jump feature in the JD and SVJ models cannot effectively capture the stylized facts of excess kurtosis
and stochastic skewness observed in the currency options market when these models are used to hedge barrier options.
In addition the NZX 15 realized volatility also displays a negative excess kurtosis
. The correlation between the NZVIX and the weekly volatility of the NZX 15 Index is 0.45, indicating a moderate positive relationship.
The standard deviation of the pressure fluctuation signals, [[sigma].sub.T], skewness, SK, and excess kurtosis
, [K.sub.R], were determined for different spouting velocities, particle diameters and bed depths.
The standardized residuals exhibit symmetric distributions, but with significant excess kurtosis
. Thus, they do not exhibit the characteristics of a normal distribution, as observed in Table 1.