Sparse Nonparametric Dynamic Graphical Models

We propose a Sparse Nonparametric Dynamic Graphical Model for financial application. We base our model on multiple CAViaR quantile regression models, and we address the issue of the quantile crossing for this type of semi-parametric models. We show how to jointly estimate the multiple quantile levels by exploiting the conditions on the parameters and setting the estimation as a linear constrained optimization problem. We employ the defined non-crossing Multiple CAViaR model as non-parametric estimation of the marginal distributions to get a sparse dynamic graphical model.