Some aspects of modeling dependence in copula-based Markov chains

Longla, Martial; Peligrad, Magda

doi:10.1016/j.jmva.2012.01.025

Cited by 32 publications

(57 citation statements)

References 12 publications

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“…For more discussions on the time series satisfying different φ-mixing conditions, we refer the readers to Bradley (2005), Longla and Peligrad (2012), and references therein. In particular, of note, Longla and Peligrad (2012) showed a variety of stationary copula-based Markov chains satisfy the φ-mixing condition in (2.3).…”

Section: Discussion On Assumption (A2)mentioning

confidence: 99%

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An Exponential Inequality for U-Statistics Under Mixing Conditions

Han

2016

J Theor Probab

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The family of U-statistics plays a fundamental role in statistics. This paper proves a novel exponential inequality for U-statistics under the time series setting. Explicit mixing conditions are given for guaranteeing fast convergence, the bound proves to be analogous to the one under independence, and extension to non-stationary time series is straightforward. The proof relies on a novel decomposition of U-statistics via exploiting the temporal correlatedness structure. Such results are of interest in many fields where high dimensional time series data are present. In particular, applications to high dimensional time series inference are discussed.

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Section: Discussion On Assumption (A2)mentioning

confidence: 99%

“…As will be shown in the next section, finite-state and vector-valued absolutely continuous data sequences of exponentially φ-mixing decaying rate satisfy (A2). Accordingly, Assumption (A2) holds for many copula-based Markov chains (Longla and Peligrad, 2012).…”

Section: Main Theoremmentioning

confidence: 99%

An Exponential Inequality for U-Statistics Under Mixing Conditions

Han

2016

J Theor Probab

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“…We have initially shown in Longla and Peligrad (2012) a result on mixtures of copulas for absolute regularity. A second result on ρ-mixing for mixtures of copulas was provided in Longla (2013).…”

Section: Motivation and Backgroundmentioning

confidence: 99%

“…We are providing here an improvement of one of our previous results. Namely, we have shown in Longla and Peligrad (2012), that Markov chains generated by a copula are φ-mixing, when the density of its absolutely continuous part is bounded away from 0. This paper provides the proof that under this condition the Markov chains are lower ψ-mixing.…”

Section: Motivation and Backgroundmentioning

confidence: 99%

“…Using the Lebesgue measure as invariant distribution after rescaling the effect of the marginal distribution, taking into account the notations from Longla and Peligrad (2012) the mixing coefficients of interest for an absolutely continuous copula and an absolutely continuous invariant distribution for the states of the stationary Markov chain that they generate are defined below. (c n (x, y) − 1)dy|dx is the absolute regularity mixing coefficient.…”

Section: Definitionsmentioning

confidence: 99%

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On mixtures of copulas and mixing coefficients

Longla

2015

Journal of Multivariate Analysis

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Please cite this article as: M. Longla, On mixtures of copulas and mixing coefficients, Journal of Multivariate Analysis (2015), http://dx. AbstractWe show that if the density of the absolutely continuous part of a copula is bounded away from zero on a set of Lebesgue measure 1, then that copula generates "lower ψ-mixing" stationary Markov chains. This conclusion implies φ-mixing, ρ-mixing, β-mixing and "interlaced ρ-mixing". We also provide some new results on the mixing structure of Markov chains generated by mixtures of copulas.

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On the Product of Random Variables and Moments of Sums Under Dependence

Peligrad

2016

High Dimensional Probability VII

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Some aspects of modeling dependence in copula-based Markov chains

Cited by 32 publications

References 12 publications

An Exponential Inequality for U-Statistics Under Mixing Conditions

An Exponential Inequality for U-Statistics Under Mixing Conditions

On mixtures of copulas and mixing coefficients

On the Product of Random Variables and Moments of Sums Under Dependence

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