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An inflated Multivariate Integer Count Hurdle model: An application to bid and ask quote dynamics

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  • Bien, Katarzyna
  • Nolte, Ingmar
  • Pohlmeier, Winfried

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.

Suggested Citation

  • Bien, Katarzyna & Nolte, Ingmar & Pohlmeier, Winfried, 2007. "An inflated Multivariate Integer Count Hurdle model: An application to bid and ask quote dynamics," CoFE Discussion Papers 07/04, University of Konstanz, Center of Finance and Econometrics (CoFE).
    • Handle: RePEc:zbw:cofedp:0704
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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, 2019. "Dynamic discrete mixtures for high frequency prices," Discussion Papers 19/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    4. Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
    5. Partha Deb & Pravin K. Trivedi & David M. Zimmer, 2009. "Dynamic Cost-offsets of Prescription Drug Expenditures: Panel Data Analysis Using a Copula-based Hurdle Model," NBER Working Papers 15191, National Bureau of Economic Research, Inc.
    6. 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.
    7. 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.
    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. 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.
    11. 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.

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    More about this item

    Keywords

    Multivariate Discrete Distributions; Conditional Inflation; Copula Functions; Truncations; Metropolized-Independence Sampler;
    All these keywords.

    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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