Identification of structural multivariate GARCH models

Christian M Hafner,Helmut Herwartz,Simone Maxand

doi:10.1016/j.jeconom.2020.07.019

Abstract

The class of multivariate GARCH models is widely used to quantify and monitor volatility and correlation dynamics of financial time series. While many specifications have been proposed in the literature, these models are typically silent about the system inherent transmission of implied orthogonalized shocks to vector returns. In a framework of non-Gaussian independent structural shocks, this paper proposes a loss statistic, based on higher order co-moments, to discriminate in a data-driven way between alternative structural assumptions about the transmission scheme, and hence identify the structural model. Consistency of identification is shown theoretically and via a simulation study. In its structural form, a four dimensional system comprising US and Latin American stock market returns points to a substantial volatility transmission from the US to the Latin American markets. The identified structural model improves the estimation of classical measures of portfolio risk, as well as corresponding variations.

Highlights

Over the past decades, modeling volatility has been one of the most rapidly growing areas of research in empirical finance
Being widely used in empirical practice for various aspects of portfolio monitoring and management, multivariate GARCH (MGARCH) models often lack an interpretation in a structural sense beyond a-priori considerations
Building upon recent advances in the data based identification of structural vector autoregression (VAR), we exploit the uniqueness of independent non-Gaussian innovations in MGARCH processes to determine covariance decompositions in a data based manner

Summary

Introduction

Over the past decades, modeling volatility has been one of the most rapidly growing areas of research in empirical finance. This development has been spurred especially by the introduction of multivariate GARCH models (MGARCH), such as the so-called VEC model of Bollerslev et al (1988), the BEKK model of Engle and Kroner (1995), or the DCC model of Engle (2002). For the purpose of measuring (co-)variance transmission in a timely manner at high frequency, Fengler and Herwartz (2018) extend this approach to a BEKK framework

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