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Simulation methods and error analysis for trawl processes and ambit fields

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  • Leonte, Dan
  • Veraart, Almut E.D.

Abstract

Trawl processes are continuous-time, stationary and infinitely divisible processes which can describe a wide range of possible serial correlation patterns in data. In this paper, we introduce new simulation algorithms for trawl processes with monotonic trawl functions and establish their error bounds and convergence properties. We extensively analyse the computational complexity and practical implementation of these algorithms and discuss which one to use depending on the type of Lévy basis. We extend the above methodology to the simulation of kernel-weighted, volatility modulated trawl processes and develop a new simulation algorithm for ambit fields. Finally, we discuss how simulation schemes previously described in the literature can be combined with our methods for decreased computational cost.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:215:y:2024:i:c:p:518-542
    DOI: 10.1016/j.matcom.2023.07.018
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    References listed on IDEAS

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    1. Wenying Huang & Ke Wang & F. Jay Breidt & Richard A. Davis, 2011. "A class of stochastic volatility models for environmental applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 32, pages 364-377, July.
    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. Michele Nguyen & Almut E. D. Veraart, 2017. "Spatio-temporal Ornstein–Uhlenbeck Processes: Theory, Simulation and Statistical Inference," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 46-80, March.
    4. 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.
    5. Kristjana Ýr Jónsdóttir & Anders Rønn-Nielsen & Kim Mouridsen & Eva B. Vedel Jensen, 2013. "Lévy-based Modelling in Brain Imaging," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 511-529, September.
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