Quantile regression for longitudinal data via the multivariate generalized hyperbolic distribution

While extensive research has been devoted to univariate quantile regression, this is considerably less the case for the multivariate (longitudinal) version, even though there are many potential applications, such as the joint examination of growth curves for two or more growth characteristics, such as body weight and length in infants. Quantile functions are easier to interpret for a population of curves than mean functions. While the connection between multivariate quantiles and the multivariate asymmetric Laplace distribution is known, it is less well known that its use for maximum likelihood estimation poses mathematical as well as computational challenges. Therefore, we study a broader family of multivariate generalized hyperbolic distributions, of which the multivariate asymmetric Laplace distribution is a limiting case. We offer an asymptotic treatment. Simulations and a data example supplement the modelling and theoretical considerations.

Uncertainty in Risk Modelling

In this thesis, we explore the uncertainty issues in risk modelling arising from the different approaches proposed in the literature and currently being used in the industry. The first type of methods that we discuss assume that the returns of the stocks follows a generalized hyperbolic distribution. Data is calibrated by the Expectation-Maximization (EM) algorithm in order to estimate the parameters in the underlying distribution. Once we have the parameters, we estimate the Value at Risk (VaR) and Expected Shortfall (ES) by using Monte Carlo simulations. Furthermore, we calibrate data to different copulas, including the Gauss Copula, the

Uncertainty in Risk Modelling

In this thesis, we explore the uncertainty issues in risk modelling arising from the different approaches proposed in the literature and currently being used in the industry. The first type of methods that we discuss assume that the returns of the stocks follows a generalized hyperbolic distribution. Data is calibrated by the Expectation-Maximization (EM) algorithm in order to estimate the parameters in the underlying distribution. Once we have the parameters, we estimate the Value at Risk (VaR) and Expected Shortfall (ES) by using Monte Carlo simulations. Furthermore, we calibrate data to different copulas, including the Gauss Copula, the

Research on Volatility of Return of Chinese Stock-Market Based on Generalized Hyperbolic Distribution Family

Financial time series often present a nonlinear characteristics, and the distribution of financial data often show fat tail and asymmetry, but this don’t match with the standpoint that time series obey normal distribution of return on assets, etc, which is considered by linear parametric modeling in the traditional linear framework. This paper has a systematic introduction of the definitions of GH distribution family and related statistical characteristics, which is based on reviewing the basic properties of the ARCH/GARCH model family and a common distribution of its disturbance. And select the Shanghai Composite Index and the Shanghai and Shenzhen (CSI) 300 index daily return rate index to estimate volatility model. GH distribution is used for further fitting to disturbance. This is done after take full account of the effective extraction of the model for the disturbance distribution information. The results show that the GH distribution can effectively fitting residuals distribution of the volatility models about series on return rate.