Modeling, simulation and inference for multivariate time series of counts using trawl processes

Veraart, Almut E. D.

doi:10.1016/j.jmva.2018.08.012

Cited by 20 publications

(15 citation statements)

References 42 publications

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“…An appealing characteristic of discrete analogues of continuous distributions is the generation of discrete pseudo random values, which only requires basic operations once the continuous distribution can be simulated. This simulation easiness is especially interesting for simulation based model evaluation [15] or parametric bootstrapping based inference [16].…”

Section: Introductionmentioning

confidence: 99%

On the Discretization of Continuous Probability Distributions Using a Probabilistic Rounding Mechanism

et al. 2021

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Most existing flexible count distributions allow only approximate inference when used in a regression context. This work proposes a new framework to provide an exact and flexible alternative for modeling and simulating count data with various types of dispersion (equi-, under-, and over-dispersion). The new method, referred to as “balanced discretization”, consists of discretizing continuous probability distributions while preserving expectations. It is easy to generate pseudo random variates from the resulting balanced discrete distribution since it has a simple stochastic representation (probabilistic rounding) in terms of the continuous distribution. For illustrative purposes, we develop the family of balanced discrete gamma distributions that can model equi-, under-, and over-dispersed count data. This family of count distributions is appropriate for building flexible count regression models because the expectation of the distribution has a simple expression in terms of the parameters of the distribution. Using the Jensen–Shannon divergence measure, we show that under the equidispersion restriction, the family of balanced discrete gamma distributions is similar to the Poisson distribution. Based on this, we conjecture that while covering all types of dispersions, a count regression model based on the balanced discrete gamma distribution will allow recovering a near Poisson distribution model fit when the data are Poisson distributed.

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Section: Introductionmentioning

confidence: 99%

On the Discretization of Continuous Probability Distributions Using a Probabilistic Rounding Mechanism

et al. 2021

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“…Count-valued time series are encountered in many fields, such as epidemiology (Wakefield, 2007;Schmidt and Pereira, 2011;Pedeli et al, 2015), environmental studies (Livsey et al, 2018;Noven et al, 2018), and finance (Fokianos et al, 2009(Fokianos et al, , 2020Pedeli and Karlis, 2013;Shephard and Yang, 2017;Veraart, 2019). Developing methods for estimation and inference for count-valued models is thus an important endeavour, and many approaches have been suggested in the literature.…”

Section: Introductionmentioning

confidence: 99%

“…This setup allows for both short-and long-memory of the IVT process. So far, IVT processes have been applied to financial data Shephard and Yang, 2017;Veraart, 2019) and to the modelling of extreme events in environmental time series (Noven et al, 2018). IVT processes are, under weak conditions, stationary and ergodic, which motivated to suggest a method of moments-based estimator for the parameters of the IVT model.…”

Section: Introductionmentioning

confidence: 99%

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

Bennedsen¹,

Lunde²,

Shephard³

et al. 2021

Preprint

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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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“…Then, they were independently introduced by Barndoff-Nielsen in [1] under the name of trawl processes. These processes were studied further in [5], [3], [10] and [14]. Trawl processes form a subclass of so-called ambit processes, which are useful in modelling of various phenomena, for example turbulence in physics, tumor growth in medicine, some aspects of financial mathematics, in particular related to volatility/intermittency.…”

Section: Introductionmentioning

confidence: 99%

Limit theorems for integrated trawl processes with symmetric Lévy bases

Talarczyk¹,

Treszczotko²

2020

Electron. J. Probab.

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We study long time behavior of integrated trawl processes introduced by Barndorff-Nielsen (2011). The trawl processes form a class of stationary infinitely divisible processes, they are described by an infinitely divisible random measure (Lévy base) and a family of shifts of a fixed set (trawl). We assume that the Lévy base is symmetric and homogeneous and that the trawl set is determined by the trawl function that decays slowly. Depending on the geometry of the trawl set and on the Lévy measure corresponding to the Lévy base we obtain various types of limits in law of the normalized integrated trawl processes for large times. The limit processes are always stable and self-similar with stationary increments. In some cases they have independent increments -they are stable Lévy processes where the index of stability depends on the parameters of the model. We show that stable limits with stability index smaller than 2 may appear even in cases when the underlying Lévy base has all its moments finite. In other cases, the limit process has dependent increments and it may be considered as a new extension of fractional Brownian motion to the class of stable processes.

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Modeling, simulation and inference for multivariate time series of counts using trawl processes

Cited by 20 publications

References 42 publications

On the Discretization of Continuous Probability Distributions Using a Probabilistic Rounding Mechanism

On the Discretization of Continuous Probability Distributions Using a Probabilistic Rounding Mechanism

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

Limit theorems for integrated trawl processes with symmetric Lévy bases

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