Integer‐valued Trawl Processes: A Class of Stationary Infinitely Divisible Processes |
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Authors: | Ole E Barndorff‐Nielsen Asger Lunde Neil Shephard Almut ED Veraart |
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Institution: | 1. The T. N.?Thiele Centre for Mathematics in Natural Science, Department of Mathematics and CREATES, Aarhus University;2. CREATES, Department of Economics and Business, Aarhus University;3. Department of Economics and Department of Statistics, Harvard University;4. Department of Mathematics, Imperial College London and CREATES, Aarhus University |
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Abstract: | 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. |
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Keywords: | Lé vy bases stationarity stochastic volatility time change trawl processes |
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