The Fiction of Full BEKK

10 Pages Posted: 20 Jul 2017

See all articles by Chia-Lin Chang

Chia-Lin Chang

National Chung Hsing University - Department of Applied Economics, Department of Finance

Michael McAleer

Erasmus University Rotterdam - Erasmus School of Economics, Econometric Institute; Tinbergen Institute; University of Tokyo - Centre for International Research on the Japanese Economy (CIRJE), Faculty of Economics

Date Written: June 30, 2017

Abstract

The purpose of the paper is to (i) show that univariate GARCH is not a special case of multivariate GARCH, specifically the Full BEKK model, except under parametric restrictions on the off-diagonal elements of the random coefficient autoregressive coefficient matrix, that are not consistent with Full BEKK, and (ii) provide the regularity conditions that arise from the underlying random coefficient autoregressive process, for which the (quasi-) maximum likelihood estimates have valid asymptotic properties under the appropriate parametric restrictions. The paper provides a discussion of the stochastic processes that lead to the alternative specifications, regularity conditions, and asymptotic properties of the univariate and multivariate GARCH models. It is shown that the Full BEKK model, which in empirical practice is estimated almost exclusively compared with Diagonal BEKK, has no underlying stochastic process that leads to its specification, regularity conditions, or asymptotic properties.

Keywords: Random coefficient stochastic process, Off-diagonal parametric restrictions, Diagonal BEKK, Full BEKK, Regularity conditions, Asymptotic properties, Conditional volatility, Univariate and multivariate models.

JEL Classification: C22, C32, C52, C58

Suggested Citation

Chang, Chia-Lin and McAleer, Michael, The Fiction of Full BEKK (June 30, 2017). Available at SSRN: https://ssrn.com/abstract=2995461 or http://dx.doi.org/10.2139/ssrn.2995461

Chia-Lin Chang (Contact Author)

National Chung Hsing University - Department of Applied Economics, Department of Finance ( email )

Taichung, Taiwan
China

Michael McAleer

Erasmus University Rotterdam - Erasmus School of Economics, Econometric Institute ( email )

Rotterdam
Netherlands

Tinbergen Institute

Rotterdam
Netherlands

University of Tokyo - Centre for International Research on the Japanese Economy (CIRJE), Faculty of Economics

Tokyo
Japan

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