In this paper we propose a multivariate quantile regression framework to forecast Value at Risk (VaR) and Expected Shortfall (ES) of multiple financial assets simultaneously, extending Taylor (2019). We generalize the Multivariate Asymmetric Laplace (MAL) joint Petrella Raponi (2019) time-varying setting, which allows us specify dynamic process for evolution both VaR ES each asset. The proposed...

In this extended abstract we define a class of distributions which we shall refer to as multivariate matrix–exponential distributions (MVME). They are defined in a natural way, inspired by the definition of univariate matrix– exponential distributions, as the distributions on R+ having a rational (multidimensional) Laplace transform. A multidimensional rational function is the fraction between ...

It is often possible to e ectively calculate cumulative distribution functions and other quantities of interest by numerically inverting Laplace transforms. However, to do so it is necessary to compute the Laplace transform values. Unfortunately, convenient explicit expressions for required transforms are often unavailable. In that event, we show that it is sometimes possible to nd continued-fr...

AbstrAct: In this article, we introduce an alternative distribution , namely Esscher transformed Laplace distribution good enough to model the file size distribution of Web servers. It exhibits asymmetry, peakedness and tail heaviness, which are common features of file size data. Esscher transformed Laplace distribution belongs to one parameter regular exponential family. We derive their repres...

We propose a new stochastic search algorithm for Gaussian graphical models called the mode oriented stochastic search. Our algorithm relies on the existence of a method to accurately and efficiently approximate the marginal likelihood associated with a graphical model when it cannot be computed in closed form. To this end, we develop a new Laplace approximation method to the normalizing constan...

In a series of papers, we discussed the solution of Laplace’s differential equation (DE) by using fractional calculus, operational calculus in the framework of distribution theory, and Laplace transform. The solutions of Kummer’s DE, which are expressed by the confluent hypergeometric functions, are obtained with the aid of the analytic continuation (AC) of Riemann–Liouville fractional derivati...

We provide a sharp nonasymptotic analysis of the rates of convergence for some standard multivariate Markov chains using spectral techniques. All chains under consideration have multivariate orthogonal polynomial as eigenfunctions. Our examples include the Moran model in population genetics and its variants in community ecology, the Dirichlet-multinomial Gibbs sampler, a class of generalized Be...

Many studies in recent time include a large number of predictor variables, but typically only a few of the predictors have significant roles. Variable selection techniques have been developed using both non-Bayesian and Bayesian approaches. Additive partial linear models (APLM) provide a flexible yet manageable extension of linear models, where some variables can have non-linear effects. We dev...

We provide a sharp non-asymptotic analysis of the rates of convergence for some standard multivariate Markov chains using spectral techniques. All chains under consideration have multivariate orthogonal polynomial as eigenfunctions. Our examples include the Moran’s model in population genetics and its variants in community ecology, the Dirichlet-Multinomial Gibbs sampler, a class of generalized...