Tail-Index Estimates in Small Samples

Huisman, Ronald; Koedijk, Kees; Kool, Clemens; Palm, Franz C.

doi:10.1198/073500101316970421

Cited by 252 publications

(200 citation statements)

References 13 publications

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“…11 (Standard errors of the 11 Generally similar (within approximately 2%) estimates of the parameters µ and σ are obtained by first estimating the tail (shape) parameter by a bias-corrected Hill estimator (Huisman et al 2001), and using ML for the remaining scale and location parameters of the GEV distribution; the right tail of the NASDAQ returns, however, shows substantially different estimates by this method.…”

Section: Implications For Measuring Financial Riskmentioning

confidence: 90%

“…3 Where the absolute level of the tail index is the key object of interest, as in Section 2.3 below, methods such as that of Huisman et al (2001) provide substantial bias reductions while retaining many of the desirable features of Hill estimation. 4 Note that this is distinct from cross-sectional dependence in extreme events across markets.…”

Section: The Extremal Indexmentioning

confidence: 99%

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Extreme dependence in the NASDAQ and S&P 500 composite indexes

Galbraith

Zernov²

2009

Applied Financial Economics

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Dependence among large observations in equity markets is usually examined using secondmoment models such as those from the GARCH or SV classes. Such models treat the entire set of returns, and tend to produce very similar estimates on the major equity markets, with a sum of estimated GARCH parameters, for example, slightly below one. Using dependence measures from extreme value theory, however, it is possible to characterize dependence among only the largest (or largest negative) financial returns; these alternative characterizations of clustering have important applications in risk management. In this paper we compare the NASDAQ and S&P in this way, and implement tests which can be used for the null hypothesis of the same degree of extreme dependence. Although GARCH-type characterizations of second-moment dependence in the two markets produce similar results, the same is not true in the extremes: we find significantly more extreme dependence in the NASDAQ returns. More generally, the study of extreme dependence may reveal contrasts which are obscured when examining the conditional second moment.

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Section: Implications For Measuring Financial Riskmentioning

confidence: 90%

Section: The Extremal Indexmentioning

confidence: 99%

Extreme dependence in the NASDAQ and S&P 500 composite indexes

Galbraith

Zernov²

2009

Applied Financial Economics

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“…Practical methods that have been developed for the estimation of the EVT index, including expansion-based estimators [6] and the well-known Hill estimator and its variants [23], can all be applied to LID (for a survey, see [24]). …”

Section: Definition 1 ([5])mentioning

confidence: 99%

The vulnerability of learning to adversarial perturbation increases with intrinsic dimensionality

Amsaleg

Bailey

Barbe

et al. 2017

2017 IEEE Workshop on Information Forensics and Security (WIFS)

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Abstract-Recent research has shown that machine learning systems, including state-of-the-art deep neural networks, are vulnerable to adversarial attacks. By adding to the input object an imperceptible amount of adversarial noise, it is highly likely that the classifier can be tricked into assigning the modified object to any desired class. It has also been observed that these adversarial samples generalize well across models. A complete understanding of the nature of adversarial samples has not yet emerged. Towards this goal, we present a novel theoretical result formally linking the adversarial vulnerability of learning to the intrinsic dimensionality of the data. In particular, our investigation establishes that as the local intrinsic dimensionality (LID) increases, 1-NN classifiers become increasingly prone to being subverted. We show that in expectation, a k-nearest neighbor of a test point can be transformed into its 1-nearest neighbor by adding an amount of noise that diminishes as the LID increases. We also provide an experimental validation of the impact of LID on adversarial perturbation for both synthetic and real data, and discuss the implications of our result for general classifiers.

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“…ii The approach has also been used in a multivariate setting examining extreme spillovers between markets 8 and estimating extreme correlations for bull and bear markets 9 . property has been documented for the extreme returns of many financial time series, such as index returns 11 , single equities (Danielsson and de Vries, 2000) 12 , foreign exchange (Huisman et al, 2001) 13 and derivatives (Cotter, 2001) 2 . The property indicates the propensity for financial time series to exhibit upside and downside returns of very large magnitude relative to the normal distribution for given probability levels.…”

Section: Theory and Estimation Methodsmentioning

confidence: 99%

Extreme global equity market risk

Cotter

Dowd²

2011

J Deriv Hedge Funds

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Publication AbstractExtreme asset price movements appear to be more pronounced over time and have major consequences for an economy's financial stability and monetary policies. This paper investigates the extreme behaviour of equity market returns and quantifies the probabilities of these losses. Taking fourteen major equity markets the study illustrates similarities and divergences in the tail returns from around the world. To do so, it applies extreme value theory to equity indices representing American, Asian and European markets. The paper finds that all markets tail realisations are adequately modelled with the fat-tailed Fréchet distribution.Furthermore tail realisations associated with the downside of a distribution are greater than those associated with the upside, and extreme returns for Asian markets are usually larger than their European and American counterparts. JEL classification: G1; G10.

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Tail-Index Estimates in Small Samples

Cited by 252 publications

References 13 publications

Extreme dependence in the NASDAQ and S&P 500 composite indexes

Extreme dependence in the NASDAQ and S&P 500 composite indexes

The vulnerability of learning to adversarial perturbation increases with intrinsic dimensionality

Extreme global equity market risk

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