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BIN Models for Trade-by-Trade Data. Modelling the Number of Trades in a Fixed Interval of Time

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  • Tina Hviid Rydberg

    (Nuffield College)

  • Neil Shephard

    (Nuffield College)

Abstract

In this paper we propose a simple time series model of the number of transactions made in intervals of length $\Delta $ seconds. We call this model the {\sf BIN} model. The properties of the {\sf BIN} model are evaluated while we explore connections between this model and Cox processes --- that is Poisson processes with random intensities. We apply the modelling framework to data on trades in IBM shares.

Suggested Citation

  • Tina Hviid Rydberg & Neil Shephard, 2000. "BIN Models for Trade-by-Trade Data. Modelling the Number of Trades in a Fixed Interval of Time," Econometric Society World Congress 2000 Contributed Papers 0740, Econometric Society.
    • Handle: RePEc:ecm:wc2000:0740
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    References listed on IDEAS

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    Cited by:

    1. Aknouche, Abdelhakim & Almohaimeed, Bader & Dimitrakopoulos, Stefanos, 2020. "Forecasting transaction counts with integer-valued GARCH models," MPRA Paper 101779, University Library of Munich, Germany, revised 11 Jul 2020.
    2. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2020. "On an integer-valued stochastic intensity model for time series of counts," MPRA Paper 105406, University Library of Munich, Germany.
    3. James McCulloch, 2007. "Relative volume as a doubly stochastic binomial point process," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 55-62.
    4. Carallo, Giulia & Casarin, Roberto & Robert, Christian P., 2024. "Generalized Poisson difference autoregressive processes," International Journal of Forecasting, Elsevier, vol. 40(4), pages 1359-1390.
    5. Quoreshi, Shahiduzzaman, 2005. "Modelling High Frequency Financial Count Data," Umeå Economic Studies 656, Umeå University, Department of Economics.
    6. Abdelhakim Aknouche & Christian Francq, 2022. "Stationarity and ergodicity of Markov switching positive conditional mean models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 436-459, May.
    7. Chiranjit Dutta & Kara Karpman & Sumanta Basu & Nalini Ravishanker, 2023. "Review of Statistical Approaches for Modeling High-Frequency Trading Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 1-48, May.
    8. Huang, Lorick & Khabou, Mahmoud, 2023. "Nonlinear Poisson autoregression and nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 201-241.
    9. Anne Leucht & Michael Neumann, 2013. "Degenerate $$U$$ - and $$V$$ -statistics under ergodicity: asymptotics, bootstrap and applications in statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 349-386, April.
    10. René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer‐Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
    11. Aknouche, Abdelhakim & Bentarzi, Wissam & Demouche, Nacer, 2017. "On periodic ergodicity of a general periodic mixed Poisson autoregression," MPRA Paper 79650, University Library of Munich, Germany.
    12. Christian H. Weiß, 2017. "On Eigenvalues of the Transition Matrix of Some Count-Data Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 997-1007, September.
    13. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos & Touche, Nassim, 2019. "Integer-valued stochastic volatility," MPRA Paper 91962, University Library of Munich, Germany, revised 04 Feb 2019.

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