Integer-valued trawl processes: A class of stationary infinitely divisible processes

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

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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.
Original languageEnglish
JournalScandinavian Journal of Statistics
Pages (from-to)693-724
Number of pages32
Publication statusPublished - 2014


  • Lévy bases
  • Stationarity
  • Stochastic volatility
  • Time change
  • Trawl processes


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