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Integer-valued Trawl Processes: A Class of Stationary Infinitely Divisible Processes

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  • Ole E. Barndorff-Nielsen
  • Asger Lunde
  • Neil Shephard
  • Almut E.D. Veraart

Abstract

type="main" xml:id="sjos12056-abs-0001"> This paper introduces a new continuous-time framework for modelling serially correlated count and integer-valued data. The key component in our new model is the class of integer-valued trawl processes, which are serially correlated, stationary, infinitely divisible processes. We analyse the probabilistic properties of such processes in detail and, in addition, study volatility modulation and multivariate extensions within the new modelling framework. Moreover, we describe how the parameters of a trawl process can be estimated and obtain promising estimation results in our simulation study. Finally, we apply our new modelling framework to high-frequency financial data.

Suggested Citation

  • Ole E. Barndorff-Nielsen & Asger Lunde & Neil Shephard & Almut E.D. Veraart, 2014. "Integer-valued Trawl Processes: A Class of Stationary Infinitely Divisible Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 693-724, September.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:3:p:693-724
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    File URL: http://hdl.handle.net/10.1111/sjos.12056
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    References listed on IDEAS

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    1. Robert Jung & A. Tremayne, 2011. "Useful models for time series of counts or simply wrong ones?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(1), pages 59-91, March.
    2. O. E. Barndorff-Nielsen & P. Reinhard Hansen & A. Lunde & N. Shephard, 2009. "Realized kernels in practice: trades and quotes," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 1-32, November.
    3. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
    4. Yunwei Cui & Robert Lund, 2009. "A new look at time series of counts," Biometrika, Biometrika Trust, vol. 96(4), pages 781-792.
    5. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    6. Ole E. Barndorff-Nielsen & David G. Pollard & Neil Shephard, 2012. "Integer-valued L�vy processes and low latency financial econometrics," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 587-605, January.
    7. Richard A. Davis & Rongning Wu, 2009. "A negative binomial model for time series of counts," Biometrika, Biometrika Trust, vol. 96(3), pages 735-749.
    8. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
    9. Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
    10. N. Bingham & Susan Pitts, 1999. "Non-parametric Estimation for the M/G/∞ Queue," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 71-97, March.
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    Cited by:

    1. Valentin Courgeau & Almut E.D. Veraart, 2022. "Asymptotic theory for the inference of the latent trawl model for extreme values," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1448-1495, December.
    2. Ole E. Barndorff-Nielsen & Orimar Sauri & Benedykt Szozda, 2017. "Selfdecomposable Fields," Journal of Theoretical Probability, Springer, vol. 30(1), pages 233-267, March.
    3. Leonte, Dan & Veraart, Almut E.D., 2024. "Simulation methods and error analysis for trawl processes and ambit fields," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 518-542.
    4. Mikkel Bennedsen & Asger Lunde & Neil Shephard & Almut E. D. Veraart, 2021. "Inference and forecasting for continuous-time integer-valued trawl processes," Papers 2107.03674, arXiv.org, revised Feb 2023.
    5. Doukhan, Paul & Jakubowski, Adam & Lopes, Silvia R.C. & Surgailis, Donatas, 2019. "Discrete-time trawl processes," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1326-1348.
    6. Mikkel Bennedsen & Asger Lunde & Neil Shephard & Almut E.D. Veraart, 2021. "Inference and forecasting for continuous-time integer-valued trawl processes and their use in financial economics," CREATES Research Papers 2021-12, Department of Economics and Business Economics, Aarhus University.
    7. Veraart, Almut E.D., 2019. "Modeling, simulation and inference for multivariate time series of counts using trawl processes," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 110-129.
    8. Bennedsen, Mikkel & Lunde, Asger & Shephard, Neil & Veraart, Almut E.D., 2023. "Inference and forecasting for continuous-time integer-valued trawl processes," Journal of Econometrics, Elsevier, vol. 236(2).
    9. Grahovac, Danijel & Leonenko, Nikolai N. & Taqqu, Murad S., 2018. "Intermittency of trawl processes," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 235-242.

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