What They Did Not Tell You About Algebraic (Non-)Existence, Mathematical (IR-)Regularity and (Non-)Asymptotic Properties of the Full BEKK Dynamic Conditional Covariance Model

Michael McAleer

No 2019-18, Documentos de Trabajo del ICAE from Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico

Abstract: Persistently high negative covariances between risky assets and hedging instruments are intended to mitigate against risk and subsequent financial losses. In the event of having more than one hedging instrument, multivariate covariances need to be calculated. Optimal hedge ratios are unlikely to remain constant using high frequency data, so it is essential to specify dynamic covariance models. 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 the paper is to analyse purported analytical developments for the most widely-used multivariate dynamic conditional covariance model to have been developed to date, namely the Full BEKK model of Baba et al. (1985), which was published as Engle and Kroner (1995). 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. The paper presents a critical analysis, discussion, evaluation and presentation of caveats relating to the Full BEKK model, and an emphasis on the numerous dos and don’ts in implementing Full BEKK in practice.

Keywords: Hedging; Covariances; Correlations; Existence; Mathematical regularity; Invertibility; Likelihood function; Statistical asymptotic properties; Caveats; Practical implementation. (search for similar items in EconPapers)
JEL-codes: C22 C32 C51 C52 C58 C62 G32 (search for similar items in EconPapers)
Pages: 13 pages
Date: 2019-03
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: What They Did Not Tell You about Algebraic (Non-) Existence, Mathematical (IR-)Regularity and (Non-) Asymptotic Properties of the Full BEKK Dynamic Conditional Covariance Model (2019)
Working Paper: What They Did Not Tell You About Algebraic (Non-)Existence, Mathematical (IR-)Regularity and (Non-)Asymptotic Properties of the Full BEKK Dynamic Conditional Covariance Model (2019)
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