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Inference and forecasting for continuous-time integer-valued trawl processes

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  • Mikkel Bennedsen
  • Asger Lunde
  • Neil Shephard
  • Almut E. D. Veraart

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, in the short memory case, asymptotic normality of this estimator. When the underlying trawl process has long memory, the asymptotic behaviour of the estimator is more involved; we present some partial results for this case. The pairwise approach further allows 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 the 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.

Suggested Citation

  • 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.
  • Handle: RePEc:arx:papers:2107.03674
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    File URL: http://arxiv.org/pdf/2107.03674
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    References listed on IDEAS

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    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.
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    1. 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.

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