TY - UNPB

T1 - Inference and forecasting for continuous-time integer-valued trawl processes and their use in financial economics

AU - Bennedsen, Mikkel

AU - Lunde, Asger

AU - Shephard, Neil

AU - Veraart, Almut E. D.

PY - 2021/7/27

Y1 - 2021/7/27

N2 - 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 asymptotic normality of this estimator. The same methods allow 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 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. We argue that integer-valued trawl processes are especially well-suited in such situations.

AB - 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 asymptotic normality of this estimator. The same methods allow 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 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. We argue that integer-valued trawl processes are especially well-suited in such situations.

KW - Integer valued trawl process

KW - Lévy basis

KW - Composite likelihood

KW - Pairwise likelihood

KW - Estimation

KW - Model selection

KW - Forecasting

M3 - Working paper

T3 - CREATES Research Paper

BT - Inference and forecasting for continuous-time integer-valued trawl processes and their use in financial economics

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -