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

Additional Metadata
Keywords Hedging, covariances, existence, mathematical regularity, inevitability, likelihood, function, statistical asymptotic properties, caveats, practical implementation
JEL Time-Series Models; Dynamic Quantile Regressions (jel C22), Time-Series Models; Dynamic Quantile Regressions (jel C32), Model Construction and Estimation (jel C51), Financial Econometrics (jel C58), Existence and Stability Conditions of Equilibrium (jel C62), Financing Policy; Capital and Ownership Structure (jel G32)
Persistent URL
Series Econometric Institute Research Papers
McAleer, M.J. (2019). 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 (No. EI2019-14). Econometric Institute Research Papers. Retrieved from