A Skewed Generalized Error Distribution And Its Application

As the price return in the financial market generally has characteristics such as skewness, kurtosis and heavy tail, proper model and distribution hypothesis should be chosen according to such characteristics of data, while most of the current distributions are not suitable.In order to solve the problem, we introduce a new class of skewed generalized error distribution (SGED), which has a long tail and a skewness. We derive analytical expressions for the pdf, cdf, quantile function, information matrix and the characteristics such as mean, variance, skewness, kurtosis etc. We also establish consistency, asymptotic normality and efficiency of the maximum likelihood estimators over a large part of the parameter space.Combined with the probit model, we discuss the influence factors of gold price and analyze the operation of investment behavior in the international gold market. The result shows that the SGED distribution can describe the volatility characteristics of the international price of gold very well, and has an improved prediction ability.