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

This paper develops likelihood-based methods for estimation, inference, model selection, and forecasting of continuous-time integer-valued trawl processes. The full likelihood processes is, in general, highly intractable, motivating the use composite methods, where we consider pairwise lieu likelihood. Maximizing data yields an estimator parameter vector model, prove consistency and, short memory case, asymptotic normality this estimator. When underlying process has long memory, behaviour is more involved; present some partial results case. approach further allows us to develop probabilistic which can be used construct predictive distribution time series. In a simulation study, document good finite sample performance associated selection procedure. Lastly, are illustrated application modelling financial bid–ask spread data, find that it beneficial carefully both marginal autocorrelation structure data.