Inference and forecasting for continuous-time integer-valued trawl processes

Mikkel Bennedsen, Asger Lunde, Neil Shephard and Almut Veraart

Journal of Econometrics, 2023, vol. 236, issue 2

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.

Keywords: Count data; Lévy basis; Pairwise likelihood; Estimation; Model selection; Forecasting (search for similar items in EconPapers)
JEL-codes: C13 C51 C52 C53 C58 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:236:y:2023:i:2:s0304407623001926

DOI: 10.1016/j.jeconom.2023.105476

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