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.
翻译:本文为估算、推论、模型选择和预测连续时间整值拖网过程制定了基于可能性的方法。总体而言,整值拖网过程的全部可能性是高度棘手的,鼓励使用综合可能性方法,我们考虑对称可能性而不是全部可能性。将数据对称可能性最大化,得出模型参数矢量的估计值,我们证明这一估计值的一致性和无症状的正常性。同样的方法使我们能够制定预测方法,可用于构建整值定值时间序列的预测分布。在模拟研究中,我们记录了基于可能性的估量器和相关模型选择程序的良好有限抽样性能。最后,在模拟和预测财务投标 - sk 扩散数据的应用中说明了这些方法,我们认为仔细模拟数据的边际分布和自动联系结构是有益的。我们认为,在这种情况下,对整值拖网程序特别适合。