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Modelling Security Market Events in Continuous Time: Intensity based, Multivariate Point Process Models

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  • Clive Bowsher

    ()
    (Nuffield College, Oxford University, Oxford, England)

Abstract

A continuous time econometric modelling framework for multivariate market event (or 'transactions') data is developed in which the model is specified via the vector stochastic intensity. This has the advantage that the conditioning sigma-field is updated continuously in time as new information arrives. We introduce the class of generalised Hawkes models which allow the estimation of the dependence of the intensity on the events of previous trading days. Analytic likelihoods are available and we show how to construct diagnostic tests based on the transformation of non-Poisson processes into standard Poisson processes using random changes of time scale. A proof of the validity of the diagnostic testing procedures is given that imposes only a very weak condition on the point process model, thus establishing their widespread applicability. A continuous time bivariate point process model of the timing of trades and mid-quote changes is presented for a NYSE stock and the empirical findings are related to the theoretical and empirical market microstructure literature.

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File URL: http://www.nuff.ox.ac.uk/economics/papers/2002/w22/NuffWPf15.pdf
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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2002-W22.

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Length: 54 pages
Date of creation: 17 Oct 2002
Date of revision:
Handle: RePEc:nuf:econwp:0222

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Web page: http://www.nuff.ox.ac.uk/economics/

Related research

Keywords: Point and counting processes; intensity; multivariate; diagnostics; goodness of fit; specification tests; change of timescale; transactions data; NYSE; NASDAQ; market microstructure;

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References

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  1. BAUWENS, Luc & HAUTSCH, Nikolaus, 2003. "Dynamic latent factor models for intensity processes," CORE Discussion Papers 2003103, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  3. Anthony D. Hall & Nikolaus Hautsch, 2004. "A Continuous-Time Measurement of the Buy-Sell Pressure in a Limit Order Book Market," Research Paper Series 121, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Robert F. Engle & Asger Lunde, 2003. "Trades and Quotes: A Bivariate Point Process," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(2), pages 159-188.
  5. Arjas, Elja & Haara, Pentti, 1988. "A note on the exponentiality of total hazards before failure," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 207-218, August.
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  7. Joel Hasbrouck, 1999. "Trading Fast and Slow: Security Market Events in Real Time," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-012, New York University, Leonard N. Stern School of Business-.
  8. Donald W.K. Andrews, 1999. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Cowles Foundation Discussion Papers 1229, Cowles Foundation for Research in Economics, Yale University.
  9. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating Density Forecasts," NBER Technical Working Papers 0215, National Bureau of Economic Research, Inc.
  10. Lee, Charles M C & Ready, Mark J, 1991. " Inferring Trade Direction from Intraday Data," Journal of Finance, American Finance Association, vol. 46(2), pages 733-46, June.
  11. Clive G. Bowsher, 2003. "Modelling Security Market Events in Continuous Time: Intensity Based, Multivariate Point Process Models," Economics Papers 2003-W03, Economics Group, Nuffield College, University of Oxford.
  12. Hall, Anthony D. & Hautsch, Nikolaus, 2007. "Modelling the buy and sell intensity in a limit order book market," Journal of Financial Markets, Elsevier, vol. 10(3), pages 249-286, August.
  13. Spierdijk, L. & Nijman, T.E. & Soest, A.H.O. van, 2002. "Modeling Comovements in Trading Intensities to Distinguish Sector and Stock Specific News," Discussion Paper 2002-69, Tilburg University, Center for Economic Research.
  14. BAUWENS, Luc & ROMBOUTS, Jeroen V.K., . "Econometrics," CORE Discussion Papers RP -1713, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  15. Glosten, Lawrence R. & Milgrom, Paul R., 1985. "Bid, ask and transaction prices in a specialist market with heterogeneously informed traders," Journal of Financial Economics, Elsevier, vol. 14(1), pages 71-100, March.
  16. 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.
  17. Luc Bauwens & Nikolaus Hautsch, 2006. "Stochastic Conditional Intensity Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(3), pages 450-493.
  18. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA.
  19. 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.
  20. Engle, Robert F. & Russell, Jeffrey R., 1997. "Forecasting the frequency of changes in quoted foreign exchange prices with the autoregressive conditional duration model," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 187-212, June.
  21. Russell, Jeffrey & Engle, Robert F, 1998. "Econometric Analysis of Discrete-Valued Irregularly-Spaced Financial Transactions Data Using a New Autoregressive Conditional Multinomial Model," University of California at San Diego, Economics Working Paper Series qt00m2c5hk, Department of Economics, UC San Diego.
  22. Grammig, Joachim & Wellner, Marc, 2002. "Modeling the interdependence of volatility and inter-transaction duration processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 369-400, February.
  23. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
  24. 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.
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