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Inference and forecasting for continuous-time integer-valued trawl processes and their use in financial economics

Author

Listed:
  • Mikkel Bennedsen

    (Department of Economics and Business Economics, Aarhus University and CREATES)

  • Asger Lunde

    (Copenhagen Economics and CREATES)

  • Neil Shephard

    (Department of Economics and Department of Statistics, Harvard University)

  • Almut E.D. Veraart

    (Imperial College London and CREATES)

Abstract

This paper develops likelihood-based methods for estimation, inference, model selection, and forecasting of continuous-time integer-valued trawl processes. The full likelihood of integer-valued trawl processes is, in general, highly intractable, motivating the use of composite likelihood methods, where we consider the pairwise likelihood in lieu of the full likelihood. Maximizing the pairwise likelihood of the data yields an estimator of the parameter vector of the model, and we prove consistency and asymptotic normality of this estimator. The same methods allow us to develop probabilistic forecasting methods, which can be used to construct the predictive distribution of integer-valued time series. In a simulation study, we document good finite sample performance of the likelihood-based estimator and the associated model selection procedure. Lastly, the methods are illustrated in an application to modelling and forecasting financial bid-ask spread data, where we find that it is beneficial to carefully model both the marginal distribution and the autocorrelation structure of the data. We argue that integer-valued trawl processes are especially well-suited in such situations.

Suggested Citation

  • 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.
  • Handle: RePEc:aah:create:2021-12
    as

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    File URL: https://repec.econ.au.dk/repec/creates/rp/21/rp21_12.pdf
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    References listed on IDEAS

    as
    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    2. 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.
    3. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Integer valued trawl process; Lévy basis; composite likelihood; pairwise likelihood; estimation; model selection; forecasting;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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