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An inflated multivariate integer count hurdle model: an application to bid and ask quote dynamics

Author

Listed:
  • Katarzyna Bien
  • Ingmar Nolte
  • Winfried Pohlmeier

Abstract

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 bivariate 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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Suggested Citation

  • Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2011. "An inflated multivariate integer count hurdle model: an application to bid and ask quote dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(4), pages 669-707, June.
    • Handle: RePEc:wly:japmet:v:26:y:2011:i:4:p:669-707
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    Cited by:

    1. Eugenio Miravete, 2014. "Testing for complementarities among countable strategies," Empirical Economics, Springer, vol. 46(4), pages 1521-1544, June.
    2. Pravin Trivedi & David Zimmer, 2017. "A Note on Identification of Bivariate Copulas for Discrete Count Data," Econometrics, MDPI, vol. 5(1), pages 1-11, February.
    3. Leopoldo Catania & Roberto Di Mari & Paolo Santucci de Magistris, 2022. "Dynamic Discrete Mixtures for High-Frequency Prices," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 559-577, April.
    4. Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
    5. Marina Gomtsyan & Céline Lévy-Leduc & Sarah Ouadah & Laure Sansonnet & Christophe Bailly & Loïc Rajjou, 2025. "Variable selection in sparse multivariate GLARMA models: application to germination control by environment," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 34(2), pages 291-324, May.
    6. Katarzyna Bień-Barkowska, 2012. "A Bivariate Copula-based Model for a Mixed Binary-Continuous Distribution: A Time Series Approach," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 4(2), pages 117-142, June.
    7. Gloria Gonzalez‐Rivera & Yun Luo & Esther Ruiz, 2020. "Prediction regions for interval‐valued time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 373-390, June.
    8. Yang Lu, 2021. "The predictive distributions of thinning‐based count processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 42-67, March.
    9. Ruben Loaiza-Maya & Michael Stanley Smith, 2017. "Variational Bayes Estimation of Discrete-Margined Copula Models with Application to Time Series," Papers 1712.09150, arXiv.org, revised Jul 2018.
    10. Gloria Gonzalez-Rivera & Yun Luo & Esther Ruiz, 2018. "Prediction Regions for Interval-valued Time Series," Working Papers 201817, University of California at Riverside, Department of Economics.
    11. Deb P & Trivedi PK & Zimmer DM, 2009. "Dynamic Cost-offsets of Prescription Drug Expenditures: Panel Data Analysis Using a Copula-based Hurdle Model," Health, Econometrics and Data Group (HEDG) Working Papers 09/15, HEDG, c/o Department of Economics, University of York.
    12. Gunther Wuyts, 2012. "The impact of aggressive orders in an order-driven market: a simulation approach," The European Journal of Finance, Taylor & Francis Journals, vol. 18(10), pages 1015-1038, November.
    13. Darolles, Serge & Fol, Gaëlle Le & Lu, Yang & Sun, Ran, 2019. "Bivariate integer-autoregressive process with an application to mutual fund flows," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 181-203.

    More about this item

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • F30 - International Economics - - International Finance - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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