Ergodicité des chaînes de Markov à valeurs dans une variété algébrique : application aux modèles GARCH multivariés

Boussama, Farid

doi:10.1016/j.crma.2006.06.027

Cited by 17 publications

(18 citation statements)

References 5 publications

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“…In particular, we show that our stochastic recurrence relation can be seen as a special case of the semi-polynomial Markov chains studied by Boussama (2006). The stationary of the model then hinges on the simple and intuitive condition that the autoregressive roots in the GAS recursion lie outside the unit circle.…”

mentioning

confidence: 84%

New HEAVY Models for Fat-Tailed Returns and Realized Covariance Kernels

Janus

Lucas²,

Opschoor³

2014

SSRN Journal

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mentioning

confidence: 84%

New HEAVY Models for Fat-Tailed Returns and Realized Covariance Kernels

Janus

Lucas²,

Opschoor³

2014

SSRN Journal

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“…If fX t g is governed by (1) then it is geometrically -mixing (Boussama 1998, cf. Basrak et al 2002a, and a variety of nonlinear GARCH processes like Asymmetric, Multiplicative, and Smooth Transition GARCH are geometrically ergodic hence -mixing (Carrasco and Chen 2002, Meitz and Saikkonen 2008, cf.…”

Section: Garch Dependencementioning

confidence: 99%

“…This, however, invariably requires a smooth error distribution (e.g. Boussama 1998, Basrak et al 2002a, Carrasco and Chen 2002.…”

Section: Tail Memory: Events and Exceedancesmentioning

confidence: 99%

Tail and Nontail Memory With Applications to Extreme Value and Robust Statistics

Hill¹

2011

Econom. Theory

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New notions of tail and non-tail dependence are used to characterize separately extremal and non-extremal information, including tail log-exceedances and events, and tail-trimmed levels. We prove Near Epoch Dependence (McLeish 1975, Gallant andWhite 1988) and L 0 -Approximability (Pötscher and Prucha 1991) are equivalent for tail events and tail-trimmed levels, ensuring a Gaussian central limit theory for important extreme value and robust statistics under general conditions. We apply the theory to characterize the extremal and nonextremal memory properties of possibly very heavy tailed GARCH processes and distributed lags. This in turn is used to verify Gaussian limits for tail index, tail dependence and tail trimmed sums of these data, allowing for Gaussian asymptotics for a new Tail-Trimmed Least Squares estimator for heavy tailed processes.

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“…There exists a c > 0 such as inf θ∈Θ k det C(θ) > c. Boussama [40] concluded the geometric ergodicity for the associated Markov…”

mentioning

confidence: 99%

“…Boussama [40] immersed the BEKK-GARCH models into the framework of general state space Markov chains and used algebraic topology to conclude the 95 geometric ergodicity of such models under regularity conditions. This work is also published in [38] with minor changes.…”

mentioning

confidence: 99%

Model identification using the Efficient Determination Criterion

Resende

Dorea

2016

Journal of Multivariate Analysis

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In the realm of the model selection context, Akaike's and Schwarz's information criteria, AIC and BIC, have been applied successfully for decades for model order identification. The Efficient Determination Criterion (EDC) is a generalization of these criteria, proposed originally to define a strongly consistent class of estimators for the dependency order of a multiple Markov chain. In this work, the EDC is generalized to partially nested models, which encompass many other order identification problems. Based on some assumptions, a class of strongly consistent estimators is established in this general environment. This framework is applied to BEKK multivariate GARCH models and, in particular, the strong consistency of the order estimator based on BIC is established for these models.

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Ergodicité des chaînes de Markov à valeurs dans une variété algébrique : application aux modèles GARCH multivariés

Cited by 17 publications

References 5 publications

New HEAVY Models for Fat-Tailed Returns and Realized Covariance Kernels

New HEAVY Models for Fat-Tailed Returns and Realized Covariance Kernels

Tail and Nontail Memory With Applications to Extreme Value and Robust Statistics

Model identification using the Efficient Determination Criterion

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