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Intraday Stock Price Dependence using Dynamic Discrete Copula Distributions

Author

Listed:
  • Siem Jan Koopman

    (VU University Amsterdam, the Netherlands)

  • Rutger Lit

    (VU University Amsterdam, the Netherlands)

  • André Lucas

    (VU University Amsterdam, the Netherlands)

Abstract

We investigate the intraday dependence pattern between tick data of stock price changes using a new time-varying model for discrete copulas. We let parameters of both the marginal models and the copula vary over time using an observation driven autoregressive updating scheme based on the score of the conditional probability mass function with respect to the time-varying parameters. We apply the model to high-frequency stock price changes expressed as discrete tick-size multiples for four liquid U.S. financial stocks. Our modeling framework is based on Skellam densities for the marginals and a range of different copula functions. We find evidence of intraday time-variation in the dependence structure. After the opening and before the close of the stock market, dependence levels are lower. We attribute this finding to more idiosyncratic trading at these times. The introduction of score driven dynamics in the dependence structure significantly increases the likelihood values of the time-varying copula model. By contrast, a fixed daily seasonal dependence pattern clearly fits the data less well.

Suggested Citation

  • Siem Jan Koopman & Rutger Lit & André Lucas, 2015. "Intraday Stock Price Dependence using Dynamic Discrete Copula Distributions," Tinbergen Institute Discussion Papers 15-037/III/DSF90, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20150037
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    File URL: https://papers.tinbergen.nl/15037.pdf
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    References listed on IDEAS

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    1. Wood, Robert A & McInish, Thomas H & Ord, J Keith, 1985. "An Investigation of Transactions Data for NYSE Stocks," Journal of Finance, American Finance Association, vol. 40(3), pages 723-739, July.
    2. Creal, Drew & Koopman, Siem Jan & Lucas, André, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 552-563.
    3. Siem Jan Koopman & André Lucas & Marcel Scharth, 2016. "Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models," The Review of Economics and Statistics, MIT Press, vol. 98(1), pages 97-110, March.
    4. Brownlees, C.T. & Gallo, G.M., 2006. "Financial econometric analysis at ultra-high frequency: Data handling concerns," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2232-2245, December.
    5. Anastasios Panagiotelis & Claudia Czado & Harry Joe, 2012. "Pair Copula Constructions for Multivariate Discrete Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1063-1072, September.
    6. Francisco Blasques & Siem Jan Koopman & André Lucas, 2014. "Information Theoretic Optimality of Observation Driven Time Series Models," Tinbergen Institute Discussion Papers 14-046/III, Tinbergen Institute.
    7. Andrew Harvey & Alessandra Luati, 2014. "Filtering With Heavy Tails," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1112-1122, September.
    8. repec:dau:papers:123456789/10898 is not listed on IDEAS
    9. André Lucas & Bernd Schwaab & Xin Zhang, 2014. "Conditional Euro Area Sovereign Default Risk," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 271-284, April.
    10. Siem Jan Koopman & Rutger Lit & André Lucas, 2014. "The Dynamic Skellam Model with Applications," Tinbergen Institute Discussion Papers 14-032/IV/DSF73, Tinbergen Institute, revised 06 Jul 2015.
    11. De Lira Salvatierra, Irving & Patton, Andrew J., 2015. "Dynamic copula models and high frequency data," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 120-135.
    12. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
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    14. Tina Hviid Rydberg & Neil Shephard, 2003. "Dynamics of Trade-by-Trade Price Movements: Decomposition and Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 2-25.
    15. Anat R. Admati, Paul Pfleiderer, 1988. "A Theory of Intraday Patterns: Volume and Price Variability," Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 3-40.
    16. 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.
    17. Ulf Schepsmeier & Jakob Stöber, 2014. "Derivatives and Fisher information of bivariate copulas," Statistical Papers, Springer, vol. 55(2), pages 525-542, May.
    18. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    19. Michael C. Munnix & Rudi Schafer & Thomas Guhr, 2010. "Impact of the tick-size on financial returns and correlations," Papers 1001.5124, arXiv.org, revised Jul 2010.
    20. Münnix, Michael C. & Schäfer, Rudi & Guhr, Thomas, 2010. "Impact of the tick-size on financial returns and correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4828-4843.
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    Cited by:

    1. Siem Jan Koopman & Rutger Lit & André Lucas, 2017. "Intraday Stochastic Volatility in Discrete Price Changes: The Dynamic Skellam Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1490-1503, October.
    2. Mamode Khan Naushad & Rumjaun Wasseem & Sunecher Yuvraj & Jowaheer Vandna, 2017. "Computing with bivariate COM-Poisson model under different copulas," Monte Carlo Methods and Applications, De Gruyter, vol. 23(2), pages 131-146, June.
    3. Francisco Blasques & Vladim'ir Hol'y & Petra Tomanov'a, 2018. "Zero-Inflated Autoregressive Conditional Duration Model for Discrete Trade Durations with Excessive Zeros," Papers 1812.07318, arXiv.org, revised Apr 2020.

    More about this item

    Keywords

    time-varying copulas; dynamic discrete data; score driven models; Skellam distribution; dynamic dependence;

    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
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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