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
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.
|Keywords||hedging, covariances, correlations, existence, mathematical regularity, invertibility, 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), Model Evaluation and Testing (jel C52), Financial Econometrics (jel C58), Existence and Stability Conditions of Equilibrium (jel C62), Financing Policy; Capital and Ownership Structure (jel G32)|
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. Retrieved from http://hdl.handle.net/1765/115762