Elliptical Distribution Family Research Papers (original) (raw)

We are interested in the parametric class of Bilinear GARCH (BL-GARCH) models which are capable of simultaneously capturing the well known properties of financial retrun se- ries, volatility clustering and leverage effects. Specifically,... more

We are interested in the parametric class of Bilinear GARCH (BL-GARCH) models which are capable of simultaneously capturing the well known properties of financial retrun se- ries, volatility clustering and leverage effects. Specifically, as it is often observed that the distribution of many financial time series data has heavy tails, heavier than the Normal distribution, we examine, in this paper, the BL-GARCH model in a general setting under some non-normal distributions. We also propose and implement a maximum likelihood estimation (MLE) methodology for parameter estimation. To evaluate the small-sample performance of this method for various models, a Monte Carlo study is conducted. Finally, the capability of within-sample estimation, using the S&P 500 daily returns, is also studied.

In this paper, we discuss the class of Bilinear GATRCH (BL-GARCH) models which are capable of capturing simultaneously two key properties of non-linear time series : volatility clustering and leverage effects. It has been observed often... more

In this paper, we discuss the class of Bilinear GATRCH (BL-GARCH) models which are capable of capturing simultaneously two key properties of non-linear time series : volatility clustering and leverage effects. It has been observed often that the marginal distributions of such time series have heavy tails ; thus we examine the BL-GARCH model in a general setting under some

In this paper, we discuss the class of Bilinear GATRCH (BL-GARCH) models which are capable of capturing simultaneously two key properties of non-linear time series : volatility clustering and leverage effects. It has been observed often... more

In this paper, we discuss the class of Bilinear GATRCH (BL-GARCH) models which are capable of capturing simultaneously two key properties of non-linear time series : volatility clustering and leverage effects. It has been observed often that the marginal distributions of such time series have heavy tails ; thus we examine the BL-GARCH model in a general setting under some

This paper proposes several parametric models to compute the portfolio VaR and CVaR in a given temporal horizon and for a given level of confidence. Firstly, we describe extension of the EWMA RiskMetrics model considering conditional... more

This paper proposes several parametric models to compute the portfolio VaR and CVaR in a given temporal horizon and for a given level of confidence. Firstly, we describe extension of the EWMA RiskMetrics model considering conditional elliptically distributed returns. Secondly, we examine several new models based on different stable Paretian distributional hypotheses of return portfolios. Finally, we discuss the applicability

Significant changes,in the insurance,and financial markets,are giving in- creasing attention to the need for developing,a standard,framework,for risk measurement. Recently, there has been growing interest among insurance and... more

Significant changes,in the insurance,and financial markets,are giving in- creasing attention to the need for developing,a standard,framework,for risk measurement. Recently, there has been growing interest among insurance and investment,experts,to focus on the use of a tail conditional expectation,be- cause it shares properties that are considered,desireable and applicable in a variety of situations. In particular, it satisfies requirements of a “coherent”

A Bayesian hierarchical modelling is proposed for the different sources of scatter occurring in archaeomagnetism, which follows the natural hierarchical sampling process implemented by laboratories in field. A comparison is made with the... more

A Bayesian hierarchical modelling is proposed for the different sources of scatter occurring in archaeomagnetism, which follows the natural hierarchical sampling process implemented by laboratories in field. A comparison is made with the stratified statistics commonly used up to now. The Bayesian statistics corrects the disturbance resulting from the variability in the number of specimens taken from each sample or site. There is no need to publish results at sample level if a descending hierarchy is verified. In this case, often verified by archaeomagnetic data, only results at site level are useful for geomagnetic reference curve building. Typically, a study with at least 20 samples will give an α95i 5 per cent close to the optimal α95i for a fixed site number mi and if errors are random with zero mean (no systematic errors). The precision on the curve itself is essentially controlled, through hierarchical elliptic statistics, by the number of reference points per window and by dating errors, rather than by the confidence angles α95ij at site level (if a descending hierarchy). The Bayesian elliptic distribution proposed reveals the influence of the window width. The moving average technique is well adapted to numerous and very well dated data evenly distributed along time. It is not a global functional approach, but a (linear) local one.

This paper proposes several parametric models to compute the portfolio VaR and CVaR in a given temporal horizon and for a given level of confidence. Firstly, we describe extension of the EWMA RiskMetrics model considering conditional... more

This paper proposes several parametric models to compute the portfolio VaR and CVaR in a given temporal horizon and for a given level of confidence. Firstly, we describe extension of the EWMA RiskMetrics model considering conditional elliptically distributed returns. Secondly, we examine several new models based on different stable Paretian distributional hypotheses of return portfolios. Finally, we discuss the applicability

Let (X,Y)(X,Y)(X,Y) be a random vector whose conditional excess probability theta(x,y):=P(Yleqy∣X>x)\theta(x,y):=P(Y\leq y | X>x)theta(x,y):=P(Yleqy∣X>x) is of interest. Estimating this kind of probability is a delicate problem as soon as xxx tends to be large, since the conditioning event... more

Let (X,Y)(X,Y)(X,Y) be a random vector whose conditional excess probability theta(x,y):=P(Yleqy∣X>x)\theta(x,y):=P(Y\leq y | X>x)theta(x,y):=P(Yleqy∣X>x) is of interest. Estimating this kind of probability is a delicate problem as soon as xxx tends to be large, since the conditioning event becomes an extreme set. Assume that (X,Y)(X,Y)(X,Y) is elliptically distributed, with a rapidly varying radial component. In this paper, three statistical procedures are proposed to estimate theta(x,y)\theta(x,y)theta(x,y) for fixed x,yx,yx,y, with xxx large. They respectively make use of an approximation result of Abdous et al. (cf. Canad. J. Statist. 33 (2005) 317--334, Theorem 1), a new second order refinement of Abdous et al.'s Theorem 1, and a non-approximating method. The estimation of the conditional quantile function theta(x,cdot)leftarrow\theta(x,\cdot)^{\leftarrow}theta(x,cdot)leftarrow for large fixed xxx is also addressed and these methods are compared via simulations. An illustration in the financial context is also given.

The paper present an explicit expression for the density of a n-dimensional random vector with a singular Elliptical distribution. Based on this, the densities of the generalized Chi-squared and generalized t distributions are derived,... more

The paper present an explicit expression for the density of a n-dimensional random vector with a singular Elliptical distribution. Based on this, the densities of the generalized Chi-squared and generalized t distributions are derived, examining the Pearson Type VII distribution and Kotz Type distribution (as specific Elliptical distributions). Finally, the results are applied to the study of the distribution of the residuals of an Elliptical linear model and the distribution of the t-statistic, based on a sample from an Elliptical population.

The serial dependency of multivariate financial data will often be filtered by considering the residuals of univariate GARCH models adapted to every single series. This is the correct filtering strategy if the multivariate process follows... more

The serial dependency of multivariate financial data will often be filtered by considering the residuals of univariate GARCH models adapted to every single series. This is the correct filtering strategy if the multivariate process follows a so-called copula based multivariate dynamic model (CMD). These multivariate dynamic models combine univariate GARCH in a linear or nonlinear way. In these models the parameters of the marginal distribution (=univariate GARCH models) and the dependence parameter are separable in the sense that they can be estimated in two or more steps. In the first step the parameters of the marginal distribution will be estimated and in the second step the parameter(s) of dependence.To the class of CMD models belong several multivariate GARCH models like the CCC and the DCC model. In contrast the BEKK model, f.e., does not belong to this class. If the BEKK model is correctly specified the above mentioned filtering strategy could fail from a theoretical point of ...