Asymptotic Theory for the Inference of the Latent Trawl Model for Extreme Values

Courgeau, Valentin; Veraart, Almut E. D.

doi:10.2139/ssrn.3527739

Cited by 3 publications

(2 citation statements)

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“…This is a special case of composite likelihood maximisation (Varin, 2008;Varin, Reid and Firth, 2011). Even with serially-dependent data, estimators have been shown to convergence asymptotically as the sample size increases (Courgeau and Veraart, 2021). Respectively, we estimate ( γ i,j cf , σ i,j cf ) for any j ∈ I by conditioning on the complement C i,c and maximising the GPD likelihood of…”

Section: Marginal Distributionsmentioning

confidence: 99%

Extreme event propagation using counterfactual theory and vine copulas

Courgeau,

Veraart

2021

Preprint

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Section: Marginal Distributionsmentioning

confidence: 99%

Extreme event propagation using counterfactual theory and vine copulas

Courgeau,

Veraart

2021

Preprint

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“…Exceptions are Shephard and Yang (2016) and Noven et al (2018). In Noven et al (2018), a pairwise likelihood was used for a hierarchical model involving a latent (Gamma-distributed) trawl process and the corresponding asymptotic theory was derived in Courgeau and Veraart (2020). However, the asymptotic theory for inference for integer-valued trawl processes which are observed directly, is not covered by these earlier papers.…”

Section: Introductionmentioning

confidence: 99%

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

Bennedsen¹,

Lunde²,

Shephard³

et al. 2021

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This paper develops likelihood-based methods for estimation, inference, model selection, and forecasting of continuous-time integer-valued trawl processes. The full likelihood of integervalued 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.

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