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Constrained QML Estimation for Multivariate Asymmetric MEM with Spillovers: The Practicality of Matrix Inequalities

Author

Listed:
  • Karanasos, Menelaos

    (Brunel University London)

  • Xu, Yongdeng

    (Cardiff Business School)

  • Yfanti, Stavroula

    (School of Business and Economics, Loughborough University)

Abstract

In this paper, we review and generalize results on the derivation of tractable non-negativity (necessary and sufficient) conditions for N-dimensional asymmetric MEM and GARCH/HEAVY models with spillovers. We show that the non-negativity constraints are translated into simple matrix inequalities, which are easily handled. In practice, these conditions may not be ful lled. To deal with these cases, we propose a constrained QML estimation. We also obtain new theoretical results about the second moment structure and the optimal forecasts of such multivariate processes. Four empirical examples are included to show the e ectiveness of the proposed method.

Suggested Citation

  • Karanasos, Menelaos & Xu, Yongdeng & Yfanti, Stavroula, 2017. "Constrained QML Estimation for Multivariate Asymmetric MEM with Spillovers: The Practicality of Matrix Inequalities," Cardiff Economics Working Papers E2017/14, Cardiff University, Cardiff Business School, Economics Section.
    • Handle: RePEc:cdf:wpaper:2017/14
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    References listed on IDEAS

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    1. Conrad, Christian, 2010. "Non-negativity conditions for the hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 157(2), pages 441-457, August.
    2. Cipollini, Fabrizio & Gallo, Giampiero M., 2010. "Automated variable selection in vector multiplicative error models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2470-2486, November.
    3. Nakatani, Tomoaki & Teräsvirta, Timo, 2008. "Positivity constraints on the conditional variances in the family of conditional correlation GARCH models," Finance Research Letters, Elsevier, vol. 5(2), pages 88-95, June.
    4. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2013. "Semiparametric Vector Mem," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(7), pages 1067-1086, November.
    5. Hautsch, Nikolaus, 2008. "Capturing common components in high-frequency financial time series: A multivariate stochastic multiplicative error model," Journal of Economic Dynamics and Control, Elsevier, vol. 32(12), pages 3978-4015, December.
    6. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    7. Manganelli, Simone, 2005. "Duration, volume and volatility impact of trades," Journal of Financial Markets, Elsevier, vol. 8(4), pages 377-399, November.
    8. Tsai, Henghsiu & Chan, Kung-Sik, 2008. "A Note On Inequality Constraints In The Garch Model," Econometric Theory, Cambridge University Press, vol. 24(3), pages 823-828, June.
    9. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-235, April.
    10. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
    11. Rasmus S. Pedersen & Anders Rahbek, 2014. "Multivariate variance targeting in the BEKK–GARCH model," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 24-55, February.
    12. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    13. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 3-27.
    14. Neil Shephard & Kevin Sheppard, 2010. "Realising the future: forecasting with high-frequency-based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 197-231.
    15. Satchell, Stephen & Knight, John, 2007. "Forecasting Volatility in the Financial Markets," Elsevier Monographs, Elsevier, edition 3, number 9780750669429.
    16. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    17. Lars Forsberg & Eric Ghysels, 2007. "Why Do Absolute Returns Predict Volatility So Well?," Journal of Financial Econometrics, Oxford University Press, vol. 5(1), pages 31-67.
    18. Jinliang Li & Chunchi Wu, 2006. "Daily Return Volatility, Bid-Ask Spreads, and Information Flow: Analyzing the Information Content of Volume," The Journal of Business, University of Chicago Press, vol. 79(5), pages 2697-2740, September.
    19. Karanasos, M. & Kartsaklas, A., 2009. "Dual long-memory, structural breaks and the link between turnover and the range-based volatility," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 838-851, December.
    20. Diamond, Douglas W. & Verrecchia, Robert E., 1987. "Constraints on short-selling and asset price adjustment to private information," Journal of Financial Economics, Elsevier, vol. 18(2), pages 277-311, June.
    21. Easley, David & O'Hara, Maureen, 1987. "Price, trade size, and information in securities markets," Journal of Financial Economics, Elsevier, vol. 19(1), pages 69-90, September.
    22. Nielsen, Heino Bohn & Rahbek, Anders, 2014. "Unit root vector autoregression with volatility induced stationarity," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 144-167.
    23. Francq, Christian & Sucarrat, Genaro, 2017. "An equation-by-equation estimator of a multivariate log-GARCH-X model of financial returns," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 16-32.
    24. N. Taylor & Y. Xu, 2017. "The logarithmic vector multiplicative error model: an application to high frequency NYSE stock data," Quantitative Finance, Taylor & Francis Journals, vol. 17(7), pages 1021-1035, July.
    25. Tomoaki Nakatani & Timo Terasvirta, 2009. "Testing for volatility interactions in the Constant Conditional Correlation GARCH model," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 147-163, March.
    26. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.
    27. Easley, David & O'Hara, Maureen, 1992. "Time and the Process of Security Price Adjustment," Journal of Finance, American Finance Association, vol. 47(2), pages 576-605, June.
    28. Francq, C. & Jiménez-Gamero, M.D. & Meintanis, S.G., 2017. "Tests for conditional ellipticity in multivariate GARCH models," Journal of Econometrics, Elsevier, vol. 196(2), pages 305-319.
    29. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    30. Henghsiu Tsai & K. S. Chan, 2007. "A Note on Non‐Negative Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 350-360, May.
    31. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
    32. Wang, Jianxin, 2007. "Foreign equity trading and emerging market volatility: Evidence from Indonesia and Thailand," Journal of Development Economics, Elsevier, vol. 84(2), pages 798-811, November.
    33. Anat R. Admati, Paul Pfleiderer, 1988. "A Theory of Intraday Patterns: Volume and Price Variability," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 3-40.
    34. Claudio, Morana, 2015. "Semiparametric Estimation of Multivariate GARCH Models," Working Papers 317, University of Milano-Bicocca, Department of Economics, revised 10 Dec 2015.
    35. Diaa Noureldin & Neil Shephard & Kevin Sheppard, 2012. "Multivariate high‐frequency‐based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 907-933, September.
    36. C. Gourieroux, 2007. "Positivity Conditions for a Bivariate Autoregressive Volatility Specification," Journal of Financial Econometrics, Oxford University Press, vol. 5(4), pages 624-636, Fall.
    37. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    38. He, Changli & Teräsvirta, Timo, 2004. "An Extended Constant Conditional Correlation Garch Model And Its Fourth-Moment Structure," Econometric Theory, Cambridge University Press, vol. 20(5), pages 904-926, October.
    39. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
    40. Conrad, Christian & Karanasos, Menelaos, 2010. "Negative Volatility Spillovers In The Unrestricted Eccc-Garch Model," Econometric Theory, Cambridge University Press, vol. 26(3), pages 838-862, June.
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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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