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Gomes, M. Ivette; Oliveira, Orlando

doi:10.1023/a:1016592028871

Cited by 102 publications

(9 citation statements)

References 21 publications

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“…This method is based on a similar algorithm as that in the dAMSE method but with a different estimation of second-order parameters dependent upon three tuning parameters, σ < τ 1 < τ 2 (Caeiro and Gomes 2016). The Hall and Welsh procedure is quite sensitive to changes in the tuning parameters, but the parameter values proposed by Hall and Welsh (σ = 0.5, τ 1 = 0.9, τ 2 = 0.95) seem to work well (Gomes and Oliveira 2001). This method may be presented in five steps (e.g., see Gomes and Oliveira 2001;Hall and Welsh 1985):…”

Section: Minimization Of the Asymptotic Mean Squared Error (Damse) Methodsmentioning

confidence: 99%

“…The Hall and Welsh procedure is quite sensitive to changes in the tuning parameters, but the parameter values proposed by Hall and Welsh (σ = 0.5, τ 1 = 0.9, τ 2 = 0.95) seem to work well (Gomes and Oliveira 2001). This method may be presented in five steps (e.g., see Gomes and Oliveira 2001;Hall and Welsh 1985):…”

Section: Minimization Of the Asymptotic Mean Squared Error (Damse) Methodsmentioning

confidence: 99%

“…In 1990, Hall introduced a bootstrap-based methodology for the estimation of the optimal tail fraction (see, e.g., Hall 1990;Gomes and Oliveira 2001). This method is applied to the Hall class of Pareto-type tails (Danielsson et al 2016).…”

Section: The Hall Single Bootstrap (Hall) Proceduresmentioning

confidence: 99%

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An Optimal Tail Selection in Risk Measurement

Just

Echaust

2021

Risks

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The appropriate choice of a threshold level, which separates the tails of the probability distribution of a random variable from its middle part, is considered to be a very complex and challenging task. This paper provides an empirical study on various methods of the optimal tail selection in risk measurement. The results indicate which method may be useful in practice for investors and financial and regulatory institutions. Some methods that perform well in simulation studies, based on theoretical distributions, may not perform well when real data are in use. We analyze twelve methods with different parameters for forty-eight world indices using returns from the period of 2000–Q1 2020 and four sub-periods. The research objective is to compare the methods and to identify those which can be recognized as useful in risk measurement. The results suggest that only four tail selection methods, i.e., the Path Stability algorithm, the minimization of the Asymptotic Mean Squared Error approach, the automated Eyeball method with carefully selected tuning parameters and the Hall single bootstrap procedure may be useful in practical applications.

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Section: Minimization Of the Asymptotic Mean Squared Error (Damse) Methodsmentioning

confidence: 99%

Section: Minimization Of the Asymptotic Mean Squared Error (Damse) Methodsmentioning

confidence: 99%

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An Optimal Tail Selection in Risk Measurement

Just

Echaust

2021

Risks

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“…Without any prior indication on k, the Weissman estimator shows a large volatility as it depends on the fraction sample k. Although the minimization of the bias and MSE can be considered as a criterion to select k, it is impractical as they are unknown. Other methods for the selection of sample fraction k can be found in Beirlant et al (1996) [6]; Dreea and Kaufmann (1998) [7]; Guillou and Hall (2001) [8]; Gomes and Oliveira (2001) [9].…”

Section: Weissman Methodsmentioning

confidence: 99%

A Method for Confidence Intervals of High Quantiles

Huang

Raney-Yan

2021

Entropy

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The high quantile estimation of heavy tailed distributions has many important applications. There are theoretical difficulties in studying heavy tailed distributions since they often have infinite moments. There are also bias issues with the existing methods of confidence intervals (CIs) of high quantiles. This paper proposes a new estimator for high quantiles based on the geometric mean. The new estimator has good asymptotic properties as well as it provides a computational algorithm for estimating confidence intervals of high quantiles. The new estimator avoids difficulties, improves efficiency and reduces bias. Comparisons of efficiencies and biases of the new estimator relative to existing estimators are studied. The theoretical are confirmed through Monte Carlo simulations. Finally, the applications on two real-world examples are provided.

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“…There is extensive literature proposing Mathematics 2020, 8,114 3 of 24 the optimal choice of threshold, corresponding to the application of automated methods. The most common methods for the adaptive choice of the threshold are based on the minimization of asymptotic mean squared error (AMSE) estimate (e.g., [31][32][33][34]). For example, Hall (1990) [35] and Danielson et al (2001) [33] use a bootstrap procedure to minimize the AMSE.…”

Section: Introductionmentioning

confidence: 99%

Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection

Echaust

Just

2020

Mathematics

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A conditional Extreme Value Theory (GARCH-EVT) approach is a two-stage hybrid method that combines a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) filter with the Extreme Value Theory (EVT). The approach requires pre-specification of a threshold separating distribution tails from its middle part. The appropriate choice of a threshold level is a demanding task. In this paper we use four different optimal tail selection algorithms, i.e., the path stability method, the automated Eye-Ball method, the minimization of asymptotic mean squared error method and the distance metric method with a mean absolute penalty function, to estimate out-of-sample Value at Risk (VaR) forecasts and compare them to the fixed threshold approach. Unlike other studies, we update the optimal fraction of the tail for each rolling window of the returns. The research objective is to verify to what extent optimization procedures can improve VaR estimates compared to the fixed threshold approach. Results are presented for a long and a short position applying 10 world stock indices in the period from 2000 to June 2019. Although each approach generates different threshold levels, the GARCH-EVT model produces similar Value at Risk estimates. Therefore, no improvement of VaR accuracy may be observed relative to the conservative approach taking the 95th quantile of returns as a threshold.

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Untitled

Cited by 102 publications

References 21 publications

An Optimal Tail Selection in Risk Measurement

An Optimal Tail Selection in Risk Measurement

A Method for Confidence Intervals of High Quantiles

Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection

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