Theoretical and Empirical Differences between Diagonal and Full BEKK for Risk Management

28 Pages Posted: 20 Jul 2017

See all articles by David E. Allen

David E. Allen

School of Mathematics and Statistics, The University of Sydney; Financial Research Network (FIRN); Department of Finance; School of Business and Law, Edith Cowan University

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: July 17, 2017

Abstract

The purpose of the paper is to explore the relative biases in the estimation of the Full BEKK model as compared with the Diagonal BEKK model, which is used as a theoretical and empirical benchmark. Chang and McAleer show that univariate GARCH is not a special case of multivariate GARCH, specifically, the Full BEKK model, and demonstrate that Full BEKK which, in practice, is estimated almost exclusively, has no underlying stochastic process, regularity conditions, or asymptotic properties. Diagonal BEKK (DBEKK) does not suffer from these limitations, and hence provides a suitable benchmark. We use simulated financial returns series to contrast estimates of the conditional variances and covariances from DBEKK and BEKK. The results of non-parametric tests suggest evidence of considerable bias in the Full BEKK estimates. The results of quantile regression analysis show there is a systematic relationship between the two sets of estimates as we move across the quantiles. Estimates of conditional variances from Full BEKK, relative to those from DBEKK, are lower in the left tail and higher in the right tail.

Keywords: DBEKK, BEKK, Regularity Conditions, Asymptotic Properties, Non-Parametric, Bias, Quantile regression

JEL Classification: C13, C21, C58

Suggested Citation

Allen, David Edmund and McAleer, Michael, Theoretical and Empirical Differences between Diagonal and Full BEKK for Risk Management (July 17, 2017). Available at SSRN: https://ssrn.com/abstract=3004319 or http://dx.doi.org/10.2139/ssrn.3004319

David Edmund Allen (Contact Author)

School of Mathematics and Statistics, The University of Sydney ( email )

School of Mathematics and Statistics F07
University of Sydney
Sydney, New South Wales 2006
Australia

HOME PAGE: http://www.maths.usyd.edu.au

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Department of Finance ( email )

Taiwan
Taiwan

School of Business and Law, Edith Cowan University

100 Joondalup Drive
Joondalup, WA 6027
Australia

HOME PAGE: http://www.dallenwapty.com

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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