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What They Did Not Tell You about Algebraic (Non-) Existence, Mathematical (IR-)Regularity, and (Non-) Asymptotic Properties of the Dynamic Conditional Correlation (DCC) Model

1,2,3,4,5
1
Department of Finance, Asia University, Taichung 41354, Taiwan
2
Discipline of Business Analytics, University of Sydney Business School, Sydney 2006, Australia
3
Econometric Institute, Erasmus School of Economics, Erasmus University, Rotterdam, 3062 PA Rotterdam, The Netherlands
4
Department of Economic Analysis and ICAE, Complutense University of Madrid, 28040 Madrid, Spain
5
Institute of Advanced Sciences, Yokohama National University, Yokohama 240-8501, Japan
J. Risk Financial Manag. 2019, 12(2), 61; https://doi.org/10.3390/jrfm12020061
Received: 11 March 2019 / Revised: 1 April 2019 / Accepted: 5 April 2019 / Published: 9 April 2019
(This article belongs to the Collection Feature Papers from Journal Editorial Board)
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Abstract

In order to hedge efficiently, persistently high negative covariances or, equivalently, correlations, between risky assets and the hedging instruments are intended to mitigate against financial risk and subsequent losses. If there is more than one hedging instrument, multivariate covariances and correlations have to be calculated. As optimal hedge ratios are unlikely to remain constant using high frequency data, it is essential to specify dynamic time-varying models of covariances and correlations. These values can either be determined analytically or numerically on the basis of highly advanced computer simulations. Analytical developments are occasionally promulgated for multivariate conditional volatility models. The primary purpose of this paper is to analyze purported analytical developments for the only multivariate dynamic conditional correlation model to have been developed to date, namely the widely used Dynamic Conditional Correlation (DCC) model. Dynamic models are not straightforward (or even possible) to translate in terms of the algebraic existence, underlying stochastic processes, specification, mathematical regularity conditions, and asymptotic properties of consistency and asymptotic normality, or the lack thereof. This paper presents a critical analysis, discussion, evaluation, and presentation of caveats relating to the DCC model, with an emphasis on the numerous dos and don’ts in implementing the DCC model, as well as a related model, in practice. View Full-Text
Keywords: hedging; covariances; correlations; existence; mathematical regularity; invertibility; likelihood function; statistical asymptotic properties; caveats; practical implementation hedging; covariances; correlations; existence; mathematical regularity; invertibility; likelihood function; statistical asymptotic properties; caveats; practical implementation
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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McAleer, M. What They Did Not Tell You about Algebraic (Non-) Existence, Mathematical (IR-)Regularity, and (Non-) Asymptotic Properties of the Dynamic Conditional Correlation (DCC) Model. J. Risk Financial Manag. 2019, 12, 61.

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