As table 2 demonstrates, this visual impression is correct: the distribution has significant leptokurtosis
The leptokurtosis or extreme tail risks in a market economy pose challenges for central banks as they obscure the loss and the reaction functions.
We further examine the degree of leptokurtosis, which is measured by the extent to which the GED parameter is less than 2, and the relative proportion of shocks or 'news' to volatility reflected by the ARCH(p) coefficients to the persistency in volatility implied by the GARCH(1) coefficient.
More importantly from the standpoint of our analytical objectives, the estimated GED parameters in all five equity markets are significantly lower than 2, indicating considerable leptokurtosis, that is, pronounced extreme tail risks.
A severely negative portfolio outcome which was a consequence of a model which did not adequately replicate reality, perhaps due to skewness or leptokurtosis
, is one explanation for "how so many people could get it wrong.
The series shows serial correlation, volatility clustering (possible GARCH) and a need for Hermite-Polynoms, controlling for leptokurtosis.
For this model, the simulation series shows leptokurtosis in the mean but not in volatility, illustrated in panel A and B.
Findings are serial correlation, volatility clustering and leptokurtosis.
Testing the SP hypothesis empirically, he finds that the SP model outperforms the normal and the stable Paretian hypotheses in that (1) the leptokurtosis
of daily asset returns is significantly reduced, (2) either transaction counts or cumulative trading volume is a good proxy for the information arrival process, and (3) both the stochastic mean and variance of the asset return process in calendar-time are deterministic functions of these proxies.
Our methodology takes into account the findings of Bekaert and Harvey (1997), who argue that when studying emerging market returns, one should be wary of the significant leptokurtosis
and skewness their stock market returns manifest.
The distribution may therefore show signs of heavy tails suggesting leptokurtosis in the time series.
Thirdly, as the ARMA-GARCH model applies a student-t distributed log-likelihood function, the estimated degree of freedom parameter may measure the degree of leptokurtosis and therefore non-normality in model residuals.