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Theoretical and Empirical Differences Between Diagonal and Full Bekk for Risk Management

Author

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  • David Allen

    (Department of Mathematics, University of Sydney, Australia)

  • Michael McAleer

    (Department of Quantitative Finance, National Tsing Hua University, Taiwan; Discipline of Business Analytics, University of Sydney Business School, Australia; Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, The Netherlands)

Abstract

The purpose of the paper is to explore the relative biases in the estimation of the Full BEKK model as compared with the Diagonal BEKK model, which is used as a theoretical and empirical benchmark. Chang and McAleer [4] show that univariate GARCH is not a special case of multivariate ARCH, specifically, the Full BEKK model, and demonstrate that Full BEKK which, in practice, is estimated almost exclusively, has no underlying stochastic process, regularity conditions, or asymptotic properties. Diagonal BEKK (DBEKK) does not suffer from these limitations, and hence provides a suitable benchmark. We use simulated financial returns series to contrast estimates of the conditional variances and covariances from DBEKK and BEKK. The results of non-parametric tests suggest evidence of considerable bias in the Full BEKK estimates. The results of quantile regression analysis show there is a systematic relationship between the two sets of estimates as we move across the quantiles. Estimates of conditional variances from Full BEKK, relative to those from DBEKK, are lower in the left tail and higher in the right tail.

Suggested Citation

  • David Allen & Michael McAleer, 2017. "Theoretical and Empirical Differences Between Diagonal and Full Bekk for Risk Management," Tinbergen Institute Discussion Papers 17-069/III, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20170069
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    References listed on IDEAS

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    Cited by:

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    3. Katsiampa, Paraskevi & Yarovaya, Larisa & Zięba, Damian, 2022. "High-frequency connectedness between Bitcoin and other top-traded crypto assets during the COVID-19 crisis," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 79(C).
    4. Katsiampa, Paraskevi, 2019. "Volatility co-movement between Bitcoin and Ether," Finance Research Letters, Elsevier, vol. 30(C), pages 221-227.
    5. Jose, Nithin & Jose, Babu & Varghese, James, 2022. "Is cross-hedging an effective strategy in equity futures market?," Finance Research Letters, Elsevier, vol. 50(C).
    6. Nathan Lael Joseph & Thi Thuy Anh Vo & Asma Mobarek & Sabur Mollah, 2020. "Volatility and asymmetric dependence in Central and East European stock markets," Review of Quantitative Finance and Accounting, Springer, vol. 55(4), pages 1241-1303, November.
    7. Zolfaghari, Mehdi & Ghoddusi, Hamed & Faghihian, Fatemeh, 2020. "Volatility spillovers for energy prices: A diagonal BEKK approach," Energy Economics, Elsevier, vol. 92(C).

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    More about this item

    Keywords

    DBEKK; BEKK; Regularity Conditions; Asymptotic Properties; Non-Parametric; Bias; Quantile regression.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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