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Energies 2018, 11(7), 1627; https://doi.org/10.3390/en11071627

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

1,2,3
and
4,5,6,7,8,9,*
1
School of Mathematics and Statistics, University of Sydney, Sydney 2006, NSW, Australia
2
Department of Finance, Asia University, Wufeng 413, Taiwan
3
School of Business and Law, Edith Cowan University, Joondalup 6027, Australia
4
Department of Finance, College of Management, Asia University, Taichung 413, Taiwan
5
Discipline of Business Analytics, Business School, University of Sydney, Sydney 2006, NSW, Australia
6
Econometric Institute Erasmus School of Economics, Erasmus University Rotterdam, 3000 Rotterdam, The Netherlands
7
Department of Economic Analysis and ICAE Complutense, University of Madrid, 28040 Madrid, Spain
8
Department of Mathematics and Statistics, University of Canterbury, Christchurch 8041, New Zealand
9
Institute of Advanced Sciences, Yokohama National University, Yokohama 240-8501, Japan
*
Author to whom correspondence should be addressed.
Received: 1 March 2018 / Revised: 26 May 2018 / Accepted: 31 May 2018 / Published: 22 June 2018
(This article belongs to the Special Issue Multivariate Modelling of Fossil Fuel and Carbon Emission Prices)
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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 et al., 2017 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 relatively lower in the left tail and higher in the right tail. The BEKK model is a commonly applied multivariate volatility model frequently used in modelling and forecasting volatilities in financial applications. Our results suggest that it is subject to considerable bias and this should be considered by potential users. View Full-Text
Keywords: DBEKK; BEKK; regularity conditions; asymptotic properties; non-parametric; bias; qantile regression DBEKK; BEKK; regularity conditions; asymptotic properties; non-parametric; bias; qantile regression
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Allen, D.E.; McAleer, M. Theoretical and Empirical Differences between Diagonal and Full BEKK for Risk Management. Energies 2018, 11, 1627.

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