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Integer‐valued Trawl Processes: A Class of Stationary Infinitely Divisible Processes
Author(s) -
BarndorffNielsen Ole E.,
Lunde Asger,
Shephard Neil,
Veraart Almut E.D.
Publication year - 2014
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12056
Subject(s) - mathematics , integer (computer science) , multivariate statistics , volatility (finance) , class (philosophy) , probabilistic logic , key (lock) , econometrics , statistics , computer science , artificial intelligence , programming language , computer security
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.