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

Artikel

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 analyze purported analytical developments for the most widely-used multivariate dynamic conditional covariance model to have been developed to date, namely the Full BEKK model, named for Baba, Engle, Kraft and Kroner. 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 the Full BEKK and related non-Diagonal BEKK models, such as Triangular BEKK and Hadamard BEKK, in practice.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Journal of Risk and Financial Management ; ISSN: 1911-8074 ; Volume: 12 ; Year: 2019 ; Issue: 2 ; Pages: 1-7 ; Basel: MDPI

Classification and Topics

• Classification: Wirtschaft ; Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes ; Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models ; Model Construction and Estimation ; Model Evaluation, Validation, and Selection ; Financial Econometrics ; Existence and Stability Conditions of Equilibrium ; Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
• Subject: hedging ; covariances ; existence ; mathematical regularity ; inevitability ; likelihood function ; statistical asymptotic properties ; caveats ; practical implementation

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): McAleer, Michael
• Event: Veröffentlichung
• (who): MDPI
• (where): Basel
• (when): 2019

Further information

• DOI: doi:10.3390/jrfm12020066
• Handle: http://hdl.handle.net/10419/238991
• Last update: 10.03.2025, 11:45 AM CET