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Dynamic conditional correlation multiplicative error processes

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  • Bodnar, Taras
  • Hautsch, Nikolaus

Abstract

We introduce a dynamic model for multivariate processes of (non-negative) high-frequency trading variables revealing time-varying conditional variances and correlations. Modeling the variables' conditional mean processes using a multiplicative error model, we map the resulting residuals into a Gaussian domain using a copula-type transformation. Based on high-frequency volatility, cumulative trading volumes, trade counts and market depth of various stocks traded at the NYSE, we show that the proposed transformation is supported by the data and allows capturing (multivariate) dynamics in higher order moments. The latter are modeled using a DCC-GARCH specification. We suggest estimating the model by composite maximum likelihood which is sufficiently flexible to be applicable in high dimensions. Strong empirical evidence for time-varying conditional (co-)variances in trading processes supports the usefulness of the approach. Taking these higher-order dynamics explicitly into account significantly improves the goodness-of-fit and out-of-sample forecasts of the multiplicative error model.

Suggested Citation

  • Bodnar, Taras & Hautsch, Nikolaus, 2016. "Dynamic conditional correlation multiplicative error processes," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 41-67.
    • Handle: RePEc:eee:empfin:v:36:y:2016:i:c:p:41-67
    DOI: 10.1016/j.jempfin.2015.12.002
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    as
    1. 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.
    2. Christian T. Brownlees & Fabrizio Cipollini & Giampiero M. Gallo, 2011. "Intra-daily Volume Modeling and Prediction for Algorithmic Trading," Journal of Financial Econometrics, Oxford University Press, vol. 9(3), pages 489-518, Summer.
    3. Lee, Tae-Hwy & Long, Xiangdong, 2009. "Copula-based multivariate GARCH model with uncorrelated dependent errors," Journal of Econometrics, Elsevier, vol. 150(2), pages 207-218, June.
    4. Bauwens, Luc & Veredas, David, 2004. "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," Journal of Econometrics, Elsevier, vol. 119(2), pages 381-412, April.
    5. Manganelli, Simone, 2005. "Duration, volume and volatility impact of trades," Journal of Financial Markets, Elsevier, vol. 8(4), pages 377-399, November.
    6. 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.
    7. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2007. "A Model for Multivariate Non-negative Valued Processes in Financial Econometrics," Econometrics Working Papers Archive wp2007_16, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    8. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
    9. repec:taf:jnlbes:v:30:y:2012:i:2:p:212-228 is not listed on IDEAS
    10. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, January.
    11. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    12. Brownlees Christian T. & Vannucci Marina, 2013. "A Bayesian approach for capturing daily heterogeneity in intra-daily durations time series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(1), pages 21-46, February.
    13. Ghysels, Eric & Gourieroux, Christian & Jasiak, Joann, 2004. "Stochastic volatility duration models," Journal of Econometrics, Elsevier, vol. 119(2), pages 413-433, April.
    14. Carnero M. Angeles & Eratalay M. Hakan, 2014. "Estimating VAR-MGARCH models in multiple steps," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(3), pages 339-365, May.
    15. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
    16. Luc Bauwens & Pierre Giot, 2000. "The Logarithmic ACD Model: An Application to the Bid-Ask Quote Process of Three NYSE Stocks," Annals of Economics and Statistics, GENES, issue 60, pages 117-149.
    17. Nikolaus Hautsch, 2012. "Econometrics of Financial High-Frequency Data," Springer Books, Springer, number 978-3-642-21925-2, April.
    18. Glosten, Lawrence R, 1994. "Is the Electronic Open Limit Order Book Inevitable?," Journal of Finance, American Finance Association, vol. 49(4), pages 1127-1161, September.
    19. Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
    20. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    21. repec:adr:anecst:y:2000:i:60:p:05 is not listed on IDEAS
    22. Meitz, Mika & Terasvirta, Timo, 2006. "Evaluating Models of Autoregressive Conditional Duration," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 104-124, January.
    23. Hautsch, Nikolaus & Okhrin, Ostap & Ristig, Alexander, 2014. "Efficient iterative maximum likelihood estimation of high-parameterized time series models," CFS Working Paper Series 450, Center for Financial Studies (CFS).
    24. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    25. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    26. BAUWENS, Luc & VEREDAS, David, 1999. "The stochastic conditional duration model: a latent factor model for the analysis of financial durations," LIDAM Discussion Papers CORE 1999058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    27. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    28. Gian Piero Aielli, 2013. "Dynamic Conditional Correlation: On Properties and Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 282-299, July.
    29. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    30. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range‐Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    31. Jondeau, Eric & Rockinger, Michael, 2006. "The Copula-GARCH model of conditional dependencies: An international stock market application," Journal of International Money and Finance, Elsevier, vol. 25(5), pages 827-853, August.
    32. Zhang, Michael Yuanjie & Russell, Jeffrey R. & Tsay, Ruey S., 2001. "A nonlinear autoregressive conditional duration model with applications to financial transaction data," Journal of Econometrics, Elsevier, vol. 104(1), pages 179-207, August.
    33. Liu, Yan & Luger, Richard, 2009. "Efficient estimation of copula-GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2284-2297, April.
    34. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2016. "Copula--based Specification of vector MEMs," Papers 1604.01338, arXiv.org.
    2. Michael Curran & Patrick O'Sullivan & Ryan Zalla, 2020. "Can Volatility Solve the Naive Portfolio Puzzle?," Papers 2005.03204, arXiv.org, revised Feb 2022.
    3. Cipollini, Fabrizio & Gallo, Giampiero M., 2025. "Multiplicative Error Models: 20 years on," Econometrics and Statistics, Elsevier, vol. 33(C), pages 209-229.
    4. Nikolaus Hautsch & Ostap Okhrin & Alexander Ristig, 2023. "Maximum-Likelihood Estimation Using the Zig-Zag Algorithm," Journal of Financial Econometrics, Oxford University Press, vol. 21(4), pages 1346-1375.
    5. Gu, Huaying & Liu, Zhixue & Weng, Yingliang, 2017. "Time-varying correlations in global real estate markets: A multivariate GARCH with spatial effects approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 460-472.
    6. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2017. "Copula–Based vMEM Specifications versus Alternatives: The Case of Trading Activity," Econometrics, MDPI, vol. 5(2), pages 1-24, April.

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    More about this item

    Keywords

    Multiplicative error model; Trading processes; Gaussian domain; DCC-GARCH; Liquidity risk;
    All these keywords.

    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
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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