Adapting extreme value statistics to financial time series: dealing with bias and serial dependence

Haan, Leo de; Mercadier, Cécile; Zhou, Chen

doi:10.1007/s00780-015-0287-6

Cited by 49 publications

(40 citation statements)

References 22 publications

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“…By contrast, Gaussian approximations of the tail empirical quantile process have been known for at least three decades; see, among others, Csörgő and Horváth [10] and Einmahl and Mason [21] as well as their more modern formulations in Drees [18] and Theorem 2.4.8 in de Haan and Ferreira [15]. These powerful asymptotic results, and their later generalizations, have been successfully used in the analysis of a number of complex statistical functionals, such as test statistics aimed at checking extreme value conditions (Dietrich et al [17], Drees et al [19], Hüsler and Li [28]), bias-corrected extreme value index estimators (de Haan et al [16]) and estimators of extreme Wang distortion risk measures (El Methni and Stupfler [23,24]).…”

Section: Introductionmentioning

confidence: 99%

Tail expectile process and risk assessment

Daouia¹,

Girard²,

Stupfler³

2020

Bernoulli

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Expectiles define a least squares analogue of quantiles. They are determined by tail expectations rather than tail probabilities. For this reason and many other theoretical and practical merits, expectiles have recently received a lot of attention, especially in actuarial and financial risk management. Their estimation, however, typically requires to consider non-explicit asymmetric least squares estimates rather than the traditional order statistics used for quantile estimation. This makes the study of the tail expectile process a lot harder than that of the standard tail quantile process. Under the challenging model of heavy-tailed distributions, we derive joint weighted Gaussian approximations of the tail empirical expectile and quantile processes. We then use this powerful result to introduce and study new estimators of extreme expectiles and the standard quantile-based expected shortfall, as well as a novel expectile-based form of expected shortfall. Our estimators are built on general weighted combinations of both top order statistics and asymmetric least squares estimates. Some numerical simulations and applications to actuarial and financial data are provided.

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Section: Introductionmentioning

confidence: 99%

Tail expectile process and risk assessment

Daouia¹,

Girard²,

Stupfler³

2020

Bernoulli

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“…And indeed, both returns on CDS spreads and stock prices feature for some series in our sample weak forms of serial dependence. However, main findings of studies conducted by Hsing (1991), Drees (2000), Einmahl et al (2014), andde Haan et al (2016) suggest the validity of EVT methods under weakly serial dependence, although the asymptotic variance of estimators may differ from the iid case. The standard error estimates we use in the test on asymptotic dependence may therefore be subject to some bias.…”

Section: Gatekeepers: Bonacich Centralitymentioning

confidence: 99%

Too Connected to Fail? Inferring Network Ties From Price Co-Movements

Bosma

Koetter

Wedow

2017

Journal of Business & Economic Statistics

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We use extreme value theory methods to infer conventionally unobservable connections between financial institutions from joint extreme movements in credit default swap spreads and equity returns. Estimated pairwise co-crash probabilities identify significant connections among up to 186 financial institutions prior to the crisis of 2007/2008. Financial institutions that were very central prior to the crisis were more likely to be bailed out during the crisis or receive the status of systemically important institutions. This result remains intact also after controlling for indicators of too-big-to-fail concerns, systemic, systematic, and idiosyncratic risks. Both credit default swap (CDS)-based and equity-based connections are significant predictors of bailouts. Supplementary materials for this article are available online.

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“…This estimator can be interpreted as a refinement of the blocks method in which the sequence v n satisfies the empirical version of condition (11), that is Z * un = Z vn , and replaces u n in (18). This specific choice of the sequence v n with v n > u n implies that our estimator, in contrast to the blocks method, consists of a ratio of asymptotically i.i.d.…”

Section: Estimation Of the Extremal Indexmentioning

confidence: 99%

“…This author derives estimators of the extremal index and studies their asymptotic and finite-sample properties. Other recent articles generalizing the extreme value theory to models with serial dependence are, for example, [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A New Family of Consistent and Asymptotically-Normal Estimators for the Extremal Index

Olmo

2015

Econometrics

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The extremal index (θ) is the key parameter for extending extreme value theory results from i.i.d. to stationary sequences. One important property of this parameter is that its inverse determines the degree of clustering in the extremes. This article introduces a novel interpretation of the extremal index as a limiting probability characterized by two Poisson processes and a simple family of estimators derived from this new characterization. Unlike most estimators for θ in the literature, this estimator is consistent, asymptotically normal and very stable across partitions of the sample. Further, we show in an extensive simulation study that this estimator outperforms in finite samples the logs, blocks and runs estimation methods. Finally, we apply this new estimator to test for clustering of extremes in monthly time series of unemployment growth and inflation rates and conclude that runs of large unemployment rates are more prolonged than periods of high inflation.

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Adapting extreme value statistics to financial time series: dealing with bias and serial dependence

Cited by 49 publications

References 22 publications

Tail expectile process and risk assessment

Tail expectile process and risk assessment

Too Connected to Fail? Inferring Network Ties From Price Co-Movements

A New Family of Consistent and Asymptotically-Normal Estimators for the Extremal Index

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