Ashis SenGupta

In the spirit of the solution of for modeling price changes in high-volatility markets for univariate commodities, here we generalize an approach to the case of modeling price changes jointly for two related commodities. Often, conditional distributions are more easily understood in financial markets, where the fluctuations in one commodity can shed significant light on the behavior of a related commodity. With this observation, we enhance and characterize the entire family of bivariate joint densities for which both the conditional distributions are specified to be of the Laplace form. Such bivariate distributions will be referred to as bivariate Laplace conditional (BLC) distributions. We study the marginals of the BLC distributions and establish that they are not only sub-Gaussian but also super-Laplacian and, hence, super-Cauchy, i.e., they have heavier tails than Gaussian distributions but lighter tails than the usual Laplace and Cauchy distributions. Distance correlation is suggested as a measure of the association between the two marginal variables, as their product moment correlation is zero but they may be non-linearly dependent. A real-life data set is analyzed to illustrate the use of BCL distributions in practice. We believe that this is the first work using conditional specifications in bivariate financial data analysis.

Generalized Laplace and discrete generalized Laplace models are described and some of their properties are reviewed. For the analysis of directional data, it is natural to consider wrapped versions of these models. A well-known result for the circular and, more recently, for multivariate circular distributions that mixing and wrapping commute, allows us to readily determine the nature of these wrapped models. Some bivariate extensions of these models are discussed, together with some consideration of the feasibility of wrapping such models. Multivariate versions of the models can be envisioned.

The problem of testing the equi-correlation coefficient of a standard symmetric multivariate normal distribution is considered. Constrained Bayesian and classical Bayes methods, using the maximum likelihood estimation and Stein’s approach, are examined. For the investigation of the obtained theoretical results and choosing the best among them, different practical examples are analyzed. The simulation results showed that the constrained Bayesian method (CBM) using Stein’s approach has the advantage of making decisions with higher reliability for testing hypotheses concerning the equi-correlation coefficient than the Bayes method. Also, the use of this approach with the probability distribution of linear combinations of chi-square random variables gives better results compared to that of using the integrated probability distributions in terms of providing both the necessary precisions as well as convenience of implementation in practice. Recommendations towards the use of the proposed methods for solving practical problems are given.

With the advent of science and technology, manifold data are playing novel and important roles in emerging real-life challenging problems. These Big Data pose new challenges in the realm of Statistical Machine Learning, e.g. in cluster analysis or unsupervised learning (in the machine learning parlour) of directional data. In this paper, a brief overview of the some of recent clustering methods enhanced for cylindrical data, spherical data and toroidal data are presented. A new distance-based method for clustering data on the torus is also indicated.