Modelling multivariate volatilies via conditionally uncorrelated components

TL;DR

This paper introduces a new multivariate volatility modeling approach using conditionally uncorrelated components, simplifying high-dimensional problems and allowing flexible univariate modeling, with proven consistency and a bootstrap test.

Contribution

It presents a novel CUC-based model for multivariate volatility that is computationally efficient, flexible, and includes a consistency proof and a bootstrap test for CUC existence.

Findings

Model effectively captures multivariate volatility with CUCs.

Computational splitting improves efficiency in high dimensions.

Method validated on simulated and real data.

Abstract

We propose to model multivariate volatility processes based on the newly defined conditionally uncorrelated components (CUCs). This model represents a parsimonious representation for matrix-valued processes. It is flexible in the sense that we may fit each CUC with any appropriate univariate volatility model. Computationally it splits one high-dimensional optimization problem into several lower-dimensional subproblems. Consistency for the estimated CUCs has been established. A bootstrap test is proposed for testing the existence of CUCs. The proposed methodology is illustrated with both simulated and real data sets.