The optimal approach for emerging markets is the one that can equally well capture both leptokurtosis
(excess kurtosis) and time-varying volatility (heteroscedasticity).
Another advantage of quantile regression over OLS regression is that the quantile regression estimates are more robust against outliers in the response measurements, which gives it an edge when handling heteroskedasticity, skewness, and leptokurtosis
in financial data.
All this volatility results in pronounced tail risks, that is, much higher leptokurtosis
in the distribution of time series of asset prices and interest rates (Orlowski, 2012; Gabrisch and Orlowski, 2011).
These facts together with a third moment different from zero and a fourth moment higher than three, indicates a non-normal distribution and leptokurtosis
. Finally for later comparisons, the Value at Risk (VaR) and expected shortfall (CVaR) numbers report percentile and expected shortfall numbers for long positions at less than 2.5%.
This method will tend to increase the numbers of zero and large returns, which will tend to increase the variance and induce leptokurtosis
. It will also tend to create negative ARCH effects, as zero returns are followed by large returns.
This indicates that a leptokurtosis
at the left, which was smaller than the value of three, means that the data distribution is normal.
To avoid the possible dependencies across different trading rules, leptokurtosis
, autocorrelation, conditional heteroskedasticity, and changing conditional means, they applied the bootstrap methodology to test and validate their empirical findings.
Comparisons of the mean scores and standard deviations of the first-order and second-order constructs of authenticity between principal's self-report and teachers' ratings also revealed that principals rated themselves significantly higher than what their teachers rated them, F (5, 54) = 4.19, p =.001; [[eta].sup.2] = .14; and that the distribution of principal's self-ratings had much higher values of leptokurtosis
than teacher ratings, which means that the variance for the principal's self-ratings was much smaller than that for the teachers' ratings.
Fortunately, there remains a compelling asset class for the more pedestrian advisor seeking leptokurtosis
in exchange-traded investments--specifically, among less liquid publicly-traded stocks.
In practice, the process will vary across studies as a function of the distributions of the belimp coordinates (with complications potentially arising from leptokurtosis
The author cautions about the use of applying VaR to measure a portfolio or an enterprise as it has limitations due to its heuristic nature, and is subject to attendant assumptions and complications as represented by skewness, leptokurtosis
and outliers (especially), and conditional volatility and conditional correlation.