Sequential Conditional Correlations: Inference and Evaluation

Abstract

This paper presents a new approach to the modeling of the conditional correlation matrix in the multivariate GARCH framework which consists in breaking it into the product of a sequence of matrices with desirable characteristics. This feature will allow for a multi step estimation procedure, thus converting a highly dimensional and intractable optimization problem into a series of simple and feasible estimations. On the wake of this simplicity it is possible to employ richer parameterizations and more complex functional forms for the single components. Because positivity is ensured by the proposed decomposition, exogenous covariates can be introduced as a simple extension.

An empirical application studying the conditional second moments of 69 selected stocks from the NASDAQ100 will show how the proposed model produces strikingly accurate measures of the conditional correlations.

Keywords: Multivariate GARCH, Conditional Correlations, High Dimensional GARCH Models, Sequential Estimation, Climber

JEL Classification: C51, C52, C61, G1