Barndorff-Nielsen, Ole E.5; Lunde, Asger6; Shephard, Neil4; Veraart, Almut6
1 Department of Mathematics, Science and Technology, Aarhus University2 Department of Economics and Business Economics, Aarhus BSS, Aarhus University3 Department of Economics and Business Economics - Center for Research in Econometric Analysis of Time Series (CREATES), Department of Economics and Business Economics, Aarhus BSS, Aarhus University4 Harvard University5 Department of Mathematics, Science and Technology, Aarhus University6 Department of Economics and Business Economics, Aarhus BSS, Aarhus University
A class of stationary infinitely divisible processes
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.
Scandinavian Journal of Statistics, 2014, Vol 41, p. 693-724
Lévy bases; Stationarity; Stochastic volatility; Time change; Trawl processes