Renat Khabibullin

Dynamic Modeling of Multivariate Distributions: Reconstructing Higher Dimensional Distributions from Smaller Ones Renat Khabibullin

The problem of dynamic joint distribution estimation is very important from both theoretical and practical points of view: econometricians would be interested in developing new techniques and approaches to model dynamic joint distributions, whereas practitioners (especially, risk and asset managers) would be interested in obtaining dynamic distributions for computing risk measures and making optimal portfolio choices. This book introduces a new sequential methodology for dynamic joint distributions modeling based on combining small-dimensional distributions into higher-dimensional ones. The new proposition uses marginal and bivariate distributions as inputs, combines them to capture the dependence between one marginal and one bivariate, and then aggregates all of the dependencies to obtain trivariate distributions. Higher-dimensional distributions are built in a similar manner from one-dimension-smaller distributions and univariate ones through compounding and then aggregating them into a single distribution. Additionally, the book demonstrates how to apply this new sequential technique to model five-dimensional distribution of DJIA constituents.