Multivariate extensions of expectiles risk measures

Maume-Deschamps, Véronique; Rullière, Didier; Said, Khalil

doi:10.1515/demo-2017-0002

Cited by 25 publications

(19 citation statements)

References 40 publications

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“…Now consider the multivariate extensions of expectiles. Herrmann et al [31] present a multivariate geometric definition of expectiles, which considers the possibility of selecting different levels of risk α for the components of the vector X. Maume-Deschamps et al [41] define two notions of multivariate expectiles: L p -expectiles and Σ-expectiles. The focus of this paper is on L p -expectiles.…”

Section: Multivariate Risk Measuresmentioning

confidence: 99%

Semi-parametric estimation of multivariate extreme expectiles

Beck

Bernardino

Mailhot

2021

Journal of Multivariate Analysis

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This paper focuses on semi-parametric estimation of multivariate expectiles for extreme levels of risk. Multivariate expectiles and their extremes have been the focus of plentiful research in recent years. In particular, it has been noted that due to the difficulty in estimating these values for elevated levels of risk, an alternative formulation of the underlying optimization problem would be necessary. However, in such a scenario, estimators have only been provided for the limiting cases of tail dependence: independence and comonotonicity. In this paper, we extend the estimation of multivariate extreme expectiles (MEEs) by providing a consistent estimation scheme for random vectors with any arbitrary dependence structure. Specifically, we show that if the upper tail dependence function, tail index, and tail ratio can be consistently estimated, then one would be able to accurately estimate MEEs. The finite-sample performance of this methodology is illustrated using both simulated and real data.

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Section: Multivariate Risk Measuresmentioning

confidence: 99%

Semi-parametric estimation of multivariate extreme expectiles

Beck

Bernardino

Mailhot

2021

Journal of Multivariate Analysis

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“…The second prospect of this work is an extension to the multidimensional framework where Y ∈ R d . On the basis of the multidimensional expectile in the paper of [17], let us introduce the conditional multidimensional expectile : Let • be a norm on R d . We denote by (Y 1 ) + the vector (Y 1 ) + = ((Y 1 ) + , .…”

Section: Some Perspectivesmentioning

confidence: 99%

On the nonparametric estimation of the functional expectile regression

Mohammedi¹,

Bouzebda

Laksaci³

2020

Comptes Rendus. Mathématique

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“…Thus, for a large class of distributions fulfilling certain moment conditions, the functionals defined according to (7) and (10) are elicitable in the sense of Gneiting (2011b). If a statistical functional of interest to the decision-maker is elicitable, the loss function associated with it can be utilized at both the computation and evaluation steps of forecasting procedures in a way similar to the LINLIN loss and the MAPE (Mean Absolute Percentage Error) accuracy measure (see Weiss and Andersen 1984;Weiss 1996;Engle and Manganelli 2004;andBruzda 2016, 2018) or the loss functions discussed recently in the context of the estimation and forecasting of financial risk (see Fissler and Ziegel 2016;Dimitriadis and Bayer 2017;Maume-Deschamps et al 2017;Patton et al 2017), even if such loss functions are not of the 'prediction error' type. 4 Example loss functions (12) and (15) are obtained if one takes φ(y) y 2 and a(y) τ y 2 in (12), and φ(y) 1 2 y 2 and a(y) 1 2 y in (15), which leads, respectively, to:…”

Section: Forecasting For Supply Chain and Logistics Operationsmentioning

confidence: 99%

Multistep quantile forecasts for supply chain and logistics operations: bootstrapping, the GARCH model and quantile regression based approaches

Bruzda

2018

Cent Eur J Oper Res

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In this paper, we discuss and compare empirically various ways of computing multistep quantile forecasts of demand, with a special emphasis on the use of the quantile regression methodology. Such forecasts constitute a basis for production planning and inventory management in logistics systems optimized according to the cycle service level approach. Different econometric methods and models are considered: direct and iterated computations, linear and nonlinear (GARCH) models, simulation and nonsimulation based procedures and parametric as well as semiparametric specifications. These methods are applied to compute multiperiod quantile forecasts of the monthly microeconomic time series from the popular M3 competition database. According to various accuracy measures for quantile predictions, the best procedures are based on simulation techniques using predictive distributions generated by either the quantile regression methodology combined with random draws from the uniform distribution or parametric and nonparametric bootstrap techniques. These methods lead to large reductions in the total costs of logistics systems as compared with non-simulation based procedures. For example, in the case of forecasting 12 months ahead, relatively short time series and a high cycle service level, the quantile regression based simulation approach reduces the average supply chain cost per unit of output by about 70-85%. At the shortest horizons, the GARCH model should be seriously considered among the preferred forecasting solutions for production and inventory planning.

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Multivariate extensions of expectiles risk measures

Cited by 25 publications

References 40 publications

Semi-parametric estimation of multivariate extreme expectiles

Semi-parametric estimation of multivariate extreme expectiles

On the nonparametric estimation of the functional expectile regression

Multistep quantile forecasts for supply chain and logistics operations: bootstrapping, the GARCH model and quantile regression based approaches

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