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An Inflated Multivariate Integer Count Hurdle Model: An Application to Bid and Ask Quote Dynamics

  • Katarzyna Bien

    ()

    (University of Konstanz)

  • Ingmar Nolte

    ()

    (University of Konstanz)

  • Winfried Pohlmeier

    ()

    (University of Konstanz)

In this paper we develop a model for the conditional inflated multivariate density of integer count variables with domain Zn. Our modelling framework is based on a copula approach and can be used for a broad set of applications where the primary characteristics of the data are: (i) discrete domain, (ii) the tendency to cluster at certain outcome values and (iii) contemporaneous dependence. These kind of properties can be found for high or ultra-high frequent data describing the trading process on financial markets. We present a straightforward method of sampling from such an inflated multivariate density through the application of an Independence Metropolis-Hastings sampling algorithm. We demonstrate the power of our approach by modelling the conditional bivari- ate density of bid and ask quote changes in a high frequency setup. We show how to derive the implied conditional discrete density of the bid-ask spread, taking quote clusterings (at multiples of 5 ticks) into account.

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File URL: http://cofe.uni-konstanz.de/Papers/dp07-04.pdf
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Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 07-04.

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Length: 26 pages
Date of creation: 28 Mar 2007
Date of revision:
Handle: RePEc:knz:cofedp:0704
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  7. repec:att:wimass:9520 is not listed on IDEAS
  8. A. Colin Cameron & Tong Li & Pravin K. Trivedi & David M. Zimmer, 2004. "Modeling the Differences in Counted Outcomes using Bivariate Copula Models: with Application to Mismeasured Counts," Working Papers 43, University of California, Davis, Department of Economics.
  9. Christie, William G & Harris, Jeffrey H & Schultz, Paul H, 1994. " Why Did NASDAQ Market Makers Stop Avoiding Odd-Eighth Quotes?," Journal of Finance, American Finance Association, vol. 49(5), pages 1841-60, December.
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  12. Patton, Andrew J, 2001. "Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula," University of California at San Diego, Economics Working Paper Series qt01q7j1s2, Department of Economics, UC San Diego.
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  16. Antoniou, Antonios & Vorlow, Constantinos E., 2005. "Price clustering and discreteness: is there chaos behind the noise?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 389-403.
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  18. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
  19. Hasbrouck, Joel, 1999. "Security bid/ask dynamics with discreteness and clustering: Simple strategies for modeling and estimation1," Journal of Financial Markets, Elsevier, vol. 2(1), pages 1-28, February.
  20. Szpiro, George G., 1998. "Tick size, the compass rose and market nanostructure," Journal of Banking & Finance, Elsevier, vol. 22(12), pages 1559-1569, December.
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