Clusters of Extreme Observations and Extremal Index Estimate in GARCH Processes

Laurini, Fabrizio

doi:10.2202/1558-3708.1225

Cited by 4 publications

(13 citation statements)

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“…The problem of estimating θ has also received some attention in the literature: Hsing (1993), Smith and Weissman (1994), Weissman and Novak (1998) and Ferro and Segers (2003). Applications of the extremal index in various scientific areas include its incorporation in calculations of the Value-at-Risk measure (Longin (2000) and Klüppelberg in Finkenstädt and Rootzén (2004)), in the study of the Nasdaq and S&P 500 indices (Galbraith and Zernov (2006)) and in the study of GARCH processes (Laurini (2004)). The estimation of the extremal index θ is an important practical problem with rapidly expanding areas of application to finance, insurance, hydrology and telecommunications, to name a few (for more details, see e.g.…”

Section: Introductionmentioning

confidence: 99%

On the Estimation of the Extremal Index Based on Scaling and Resampling

Hamidieh

Stoev

Michailidis

2009

Journal of Computational and Graphical Statistics

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The extremal index parameter θ characterizes the degree of local dependence in the extremes of a stationary time series and has important applications in a number of areas, such as hydrology, telecommunications, finance, and environmental studies. In this study, a novel estimator for θ based on the asymptotic scaling of block-maxima and resampling is introduced. It is shown to be consistent and asymptotically normal for a large class of m-dependent time series. Further, a procedure for the automatic selection of its tuning parameter is developed and different types of confidence intervals that prove useful in practice proposed. The performance of the estimator is examined through simulations, which show its highly competitive behavior. Finally, the estimator is applied to three real datasets of daily crude oil prices, daily returns of the S&P 500 stock index, and high-frequency, intraday traded volumes of a stock. These applications demonstrate additional diagnostic features of statistical plots based on the new estimator. Supplementary materials including an appendix with complete proofs, the crude oil dataset, and an R-script implementing the estimators are available online.

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Section: Introductionmentioning

confidence: 99%

On the Estimation of the Extremal Index Based on Scaling and Resampling

Hamidieh

Stoev

Michailidis

2009

Journal of Computational and Graphical Statistics

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“…All of these studies detect exceedances based on only the return threshold. Since our research is aimed at understanding the relation between return correlations and volatility during extreme market conditions, we extend this line of research by applying the two‐threshold method developed by Laurini (2004), using extreme value theory.…”

Section: A Brief Review Of Related Literaturementioning

confidence: 99%

“…Whereas, Ang and Bekaert (2002) and Ang and Chen (2002) find that the correlation between extreme returns increases with volatility, Longin and Solnik (2001) find that this correlation is not related to market volatility per se but to the market trend. This paper re‐examines the relation between extreme return correlation and return volatility, in the context of US indexes, by detecting clusters of extreme returns using return and volatility thresholds based on an algorithm suggested in Laurini (2004).…”

Section: Introductionmentioning

confidence: 99%

“…These returns along with conditional volatilities estimated using a GARCH (1, 1) model serve as inputs to the two‐threshold algorithm[4]. Laurini (2004) shows that the algorithm statistically detects a mapping of independent extreme return clusters to the information that causes it. We rely on this feature of the algorithm and analyze the extent of overlap between clusters across the three indices.…”

Section: Introductionmentioning

confidence: 99%

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Extreme return correlation and volatility: a two‐threshold approach

Sankaran

Nguyen

Harikumar

2012

American Journal of Business

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PurposeThe purpose of this paper is to examine the relation between extreme return correlation and return volatility, in the context of US stock indexes, by detecting clusters of extreme returns using return and volatility thresholds based on an algorithm suggested in Laurini.Design/methodology/approachThe daily returns and conditional volatilities estimated using GARCH (1, 1) serve as inputs to the two threshold algorithm that detects extreme return clusters. The analysis of the relation between correlation and volatility is then based on the extent of overlapping extreme return clusters across DJIA, S&P 500 and NASDAQ composite.FindingsIt is found that the correlation positive extreme returns within overlapping clusters significantly increases with volatility between DJIA and S&P 500. The authors did not find any significant change in the pair‐wise correlation between the positive extreme returns within overlapping clusters in each of these indexes with those of NASDAQ composite.Originality/valuePrior researches examine extreme returns by using a return threshold and have found mixed results on the relation between correlation and volatility. This paper examines the relation between correlation and volatility between clusters of extreme returns and provides consistent results that are of vital interest to investors.

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“…When declustering is obtained with the twothresholds method, the low threshold c is set to the 50% of the marginal distribution of the scaled residuals. However, as pointed out by Laurini (2004) and Laurini and Tawn (2003), this choice is unimportant.…”

Section: Dependent Sequences and Declusteringmentioning

confidence: 99%

Regular Variation and Extremal Dependence of GARCH Residuals with Application to Market Risk Measures

Laurini

Tawn

2008

Econometric Reviews

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Stock returns exhibit heavy tails and volatility clustering. These features, motivating the use of GARCH models, make it difficult to predict times and sizes of losses that might occur. Estimation of losses, like the Value-at-Risk, often assume that returns, normalized by the level of volatility, are Gaussian. Often under ARMA-GARCH modeling, such scaled returns are heavy tailed and show extremal dependence, whose strength reduces when increasing extreme levels. We model heavy tails of scaled returns with generalized Pareto distributions, while extremal dependence can be reduced by declustering data.Declustering, Expected shortfalls, Extremal dependence, Generalized Pareto distribution, Regular variation, Value-at-Risk, C22, C53,

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Clusters of Extreme Observations and Extremal Index Estimate in GARCH Processes

Cited by 4 publications

References 0 publications

On the Estimation of the Extremal Index Based on Scaling and Resampling

On the Estimation of the Extremal Index Based on Scaling and Resampling

Extreme return correlation and volatility: a two‐threshold approach

Regular Variation and Extremal Dependence of GARCH Residuals with Application to Market Risk Measures

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