Inference and forecasting for continuous-time integer-valued trawl processes
File(s)
Accepted version
Author(s)
Bennedsen, Mikkel
Shephard, Neil
Lunde, Asger
Veraart, Almut
Type
Journal Article
Abstract
This paper develops likelihood-based methods for estimation, inference, model selection, and forecasting of continuous-time integer-valued trawl processes. The full likelihood of integer-valued trawl processes is, in general, highly intractable, motivating the use of composite likelihood methods, where we consider the pairwise likelihood in lieu of the full likelihood. Maximizing the pairwise likelihood of the data yields an estimator of the parameter vector of the model, and we prove consistency and, in the short memory case, asymptotic normality of this estimator. When the underlying trawl process has long memory, the asymptotic behaviour of the estimator is more involved; we present some partial results for this case. The pairwise approach further allows us to develop probabilistic forecasting methods, which can be used to construct the predictive distribution of integer-valued time series. In a simulation study, we document the good finite sample performance of the likelihood-based estimator and the associated model selection procedure. Lastly, the methods are illustrated in an application to modelling and forecasting financial bid–ask spread data, where we find that it is beneficial to carefully model both the marginal distribution and the autocorrelation structure of the data.
Date Issued
2023-10-01
Date Acceptance
2023-05-23
Citation
Journal of Econometrics, 2023, 236 (2)
ISSN
0304-4076
Publisher
Elsevier
Journal / Book Title
Journal of Econometrics
Volume
236
Issue
2
Copyright Statement
Copyright © Elsevier Ltd. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
Publication Status
Published
Rights Embargo Date
2025-07-05
Article Number
ARTN 105476
Date Publish Online
2023-07-06