Mixing Properties of Multivariate Infinitely Divisible Random Fields

Passeggeri, Riccardo; Veraart, Almut E. D.

doi:10.1007/s10959-018-0864-7

Cited by 8 publications

(3 citation statements)

References 20 publications

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“…However, we note that the limits in (4.9) and (4.10) are of mixed Gaussian type. Conditions which ensure the ergodicity of an ambit field with a deterministic kernel can be found in Theorem 3.6 [49] whereas for the case of a non-deterministic kernel this remains an open problem.…”

Section: Sample Moments Of Ambit Fieldsmentioning

confidence: 99%

Central limit theorems for stationary random fields under weak dependence with application to ambit and mixed moving average fields

Curato¹,

Stelzer²,

Ströh³

2020

Preprint

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We obtain central limit theorems for stationary random fields which are based on the use of a novel measure of dependence called θ-lex weak dependence. We discuss hereditary properties for θ-lex and η-weak dependence and illustrate the possible applications of the weak dependence notions to the study of the asymptotic properties of stationary random fields. Our general results are applied to mixed moving average fields (MMAF in short) and ambit fields. We show general conditions such that MMAF and ambit fields, with the volatility field being an MMAF or a p-dependent random field, are weakly dependent. For all the aforementioned models, we give a complete characterization of their weak dependence coefficients and sufficient conditions to obtain asymptotic normality of their sample moments. Finally, we give explicit computations of the weak dependence coefficients in the case of MSTOU and CARMA fields.

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Section: Sample Moments Of Ambit Fieldsmentioning

confidence: 99%

Central limit theorems for stationary random fields under weak dependence with application to ambit and mixed moving average fields

Curato¹,

Stelzer²,

Ströh³

2020

Preprint

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“…Spatio-temporal stationarity and mixing properties are useful properties to establish the consistency of moment-based estimators such as the GMM estimators which we construct in Section 5. The following definition is adapted from Passeggeri & Veraart (2017):…”

Section: Mixing Propertiesmentioning

confidence: 99%

“…The next result corresponds to the one-dimensional case in Theorem 3.6. of Passeggeri & Veraart (2017):…”

Section: Mixing Propertiesmentioning

confidence: 99%

Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein–Uhlenbeck processes

Nguyen

Veraart

2018

Stochastics

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While short-range dependence is widely assumed in the literature for its simplicity, long-range dependence is a feature that has been observed in data from finance, hydrology, geophysics and economics. In this paper, we extend a Lévy-driven spatio-temporal Ornstein-Uhlenbeck process by randomly varying its rate parameter to model both short-range and longrange dependence. This particular set-up allows for non-separable spatio-temporal correlations which are desirable for real applications, as well as flexible spatial covariances which arise from the shapes of influence regions. Theoretical properties such as spatio-temporal stationarity and second-order moments are established. An isotropic g-class is also used to illustrate how the memory of the process is related to the probability distribution of the rate parameter. We develop a simulation algorithm for the compound Poisson case which can be used to approximate other Lévy bases. The generalised method of moments is used for inference and simulation experiments are conducted with a view towards asymptotic properties.

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