This paper provides a new empirical guidance for modeling a skewed and fat-tailed error distribution underlying the traditional GARCH models for equity returns based on empirical findings on Realized Volatility (RV), constructed from the summation of higher-frequency squared (demeaned) returns. Based on an 80-year sample of U.S. daily stock market returns, I find that the distribution of monthl...

A b s t r a c t. The unbiased estimator of risk of the orthogonally invariant es-timator of the skew-symmetric normal mean matrix is obtained, and a class of minimax estimators and their order-preserving modification are proposed. The estimators have applications in paired comparisons model. A Monte Carlo study to compare the risks of the estimators is given.

A new class of densities for modelling non-negative data, which is based on the skew-symmetric family distributions proposed by Azzalini introduced.We focus model generated skew-normal distribution, called Extended Half Skew-Normal distribution. Its relevant properties are studied. These pdf, cdf, moments, mgf, and stochastic representation. The parameters estimated moment maximum likelihood me...