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Discrete-time trawl processes

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  • Doukhan, Paul
  • Jakubowski, Adam
  • Lopes, Silvia R.C.
  • Surgailis, Donatas

Abstract

We introduce a class of discrete time stationary trawl processes taking real or integer values and written as sums of past values of independent ‘seed’ processes on shrinking intervals (‘trawl heights’). Related trawl processes in continuous time were studied in Barndorff-Nielsen et al. (2011, 2014).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:4:p:1326-1348
    DOI: 10.1016/j.spa.2018.05.004
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    References listed on IDEAS

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    1. Vasiliki Christou & Konstantinos Fokianos, 2014. "Quasi-Likelihood Inference For Negative Binomial Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 55-78, January.
    2. Leipus, Remigijus & Paulauskas, Vygantas & Surgailis, Donatas, 2005. "Renewal regime switching and stable limit laws," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 299-327.
    3. 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.
    4. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2014. "Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1011-1035.
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    Cited by:

    1. 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).

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    More about this item

    Keywords

    Trawl process; Integer-valued time series; Long memory; Distributional short-range dependence; Fractional Brownian motion; Stable Lévy process; Functional convergence; Skorokhod’s M1 topology;
    All these keywords.

    JEL classification:

    • M1 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration

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