Goodness-of-Fit Tests for Multivariate Copula-Based Time Series Models

Berghaus, Betina; Bücher, Axel

doi:10.1017/s0266466615000419

Cited by 11 publications

(7 citation statements)

References 48 publications

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“…the assertion follows from Lemma 7.4, Lemma C.8 in Berghaus and Bücher (2017) and the continuous mapping theorem.…”

Section: Auxiliary Lemmas For the Proof Of Theorem 41 -Disjoint Blocksmentioning

confidence: 74%

Method of moments estimators for the extremal index of a stationary time series

Bücher¹,

Jennessen²

2019

Preprint

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The extremal index θ, a number in the interval [0, 1], is known to be a measure of primal importance for analyzing the extremes of a stationary time series. New rankbased estimators for θ are proposed which rely on the construction of approximate samples from the exponential distribution with parameter θ that is then to be fitted via the method of moments. The new estimators are analyzed both theoretically as well as empirically through a large-scale simulation study. In specific scenarios, in particular for time series models with θ ≈ 1, they are found to be superior to recent competitors from the literature.

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“…the assertion follows from Lemma 7.4, Lemma C.8 in Berghaus and Bücher (2017) and the continuous mapping theorem.…”

Section: Auxiliary Lemmas For the Proof Of Theorem 41 -Disjoint Blocksmentioning

confidence: 74%

Method of moments estimators for the extremal index of a stationary time series

Bücher¹,

Jennessen²

2019

Preprint

Self Cite

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“…• Bootstrap asymptotic validity in the form of Assertions (a) or (b) is less frequently encountered in the literature, although, as discussed in the introduction, it may be argued that this unconditional formulation is more intuitive and easy to work with. It is proved for example in Genest and Rémillard (2008) (for M = 1), Rémillard and Scaillet (2009), Segers (2012), Genest and Nešlehová (2014), Berghaus and Bücher (2017) and Bücher and Kojadinovic (2016a,b), among many others, for various stochastic processes arising in statistical tests on copulas or for assessing stationarity. • As mentioned in the introduction, note that Assertions (b) and (c) are known to be equivalent for the special case of the multiplier CLT for the general empirical process based on i.i.d.…”

Section: )mentioning

confidence: 96%

A Note on Conditional Versus Joint Unconditional Weak Convergence in Bootstrap Consistency Results

Bücher

Kojadinovic

2018

J Theor Probab

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The consistency of a bootstrap or resampling scheme is classically validated by weak convergence of conditional laws. However, when working with stochastic processes in the space of bounded functions and their weak convergence in the Hoffmann-Jørgensen sense, an obstacle occurs: due to possible non-measurability, neither laws nor conditional laws are well-defined. Starting from an equivalent formulation of weak convergence based on the bounded Lipschitz metric, a classical circumvent is to formulate bootstrap consistency in terms of the latter distance between what might be called a conditional law of the (nonmeasurable) bootstrap process and the law of the limiting process. The main contribution of this note is to provide an equivalent formulation of bootstrap consistency in the space of bounded functions which is more intuitive and easy to work with. Essentially, the equivalent formulation consists of (unconditional) weak convergence of the original process jointly with an arbitrary large number of bootstrap replicates. As a by-product, we provide two equivalent formulations of bootstrap consistency for R d -valued statistics: the first in terms of (unconditional) weak convergence of the statistic jointly with its bootstrap replicates, the second in terms of convergence in probability of the empirical distribution function of the bootstrap replicates. Finally, the asymptotic validity of bootstrap-based confidence intervals and tests is briefly revisited, with particular emphasis on the, in practice unavoidable, Monte Carlo approximation of conditional quantiles.

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“…Therefore, any absolute moment of the second factor of the right-hand side in (5.3) converges. Further, it is shown in Example 6.1 in Berghaus and Bücher (2017), see the proof of their Condition 2.1(vi) holds, that lim sup n→∞ E Zδ n,1 < ∞ for any δ > 0. Along with inequality (5.3), Hölder's inequality implies that Condition (B10) holds.…”

Section: Assessing the Serial Dependencementioning

confidence: 97%

Statistics for Heteroscedastic Time Series Extremes

Bücher¹,

Jennessen²

2022

Preprint

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Einmahl, de Haan and Zhou (2016, Journal of the Royal Statistical Society: Series B, 78(1), 31-51) recently introduced a stochastic model that allows for heteroscedasticity of extremes. The model is extended to the situation where the observations are serially dependent, which is crucial for many practical applications. We prove a local limit theorem for a kernel estimator for the scedasis function, and a functional limit theorem for an estimator for the integrated scedasis function. We further prove consistency of a bootstrap scheme that allows to test for the null hypothesis that the extremes are homoscedastic. Finally, we propose an estimator for the extremal index governing the dynamics of the extremes and prove its consistency. All results are illustrated by Monte Carlo simulations. An important intermediate result concerns the sequential tail empirical process under serial dependence.

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Goodness-of-Fit Tests for Multivariate Copula-Based Time Series Models

Cited by 11 publications

References 48 publications

Method of moments estimators for the extremal index of a stationary time series

Method of moments estimators for the extremal index of a stationary time series

A Note on Conditional Versus Joint Unconditional Weak Convergence in Bootstrap Consistency Results

Statistics for Heteroscedastic Time Series Extremes

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