Likelihood-based scoring rules for comparing density forecasts in tails

Diks, Cees; Panchenko, Valentyn; Dijk, Dick van

doi:10.1016/j.jeconom.2011.04.001

Cited by 138 publications

(191 citation statements)

References 58 publications

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“…In a related context, albeit for evaluation, Diks et al (2011) discuss the weighted logarithmic scoring rule, w t (y t+1 ) log q it (y t+1 ), where the weight function w t (y t+1 ) emphasises regions of the density of interest; one possibility, as in (30), is that w t (y t+1 ) = I (r s−1 ≤ y t+1 < r s ).…”

Section: Scoring Rulesmentioning

confidence: 99%

“…In order to facilitate interpretation, which might be helpful in some applications, we draw on Amisano & Giacomini (2007) and Diks et al (2011) who consider weighted scoring rules and suggest the following restricted variant of our method. 4…”

Section: Extensions: Interpreting the Weightsmentioning

confidence: 99%

“…As discussed by Diks et al (2011), the weighted logarithmic scoring rule, w t (y t+1 ) log q it (y t+1 ), used in (37) is not proper (see also Gneiting & Ranjan (2011)); i.e., there can exist incorrect density forecasts that would receive a higher average score than the actual (true) conditional density. Therefore, following Diks et al (2011), one might modify (37) and consider use of the conditional likelihood score function, given bỹ…”

Section: Extensions: Interpreting the Weightsmentioning

confidence: 99%

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Generalised density forecast combinations

Kapetanios

Mitchell

Price

et al. 2015

Journal of Econometrics

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Density forecast combinations are becoming increasingly popular as a means of improving forecast 'accuracy', as measured by a scoring rule. In this paper we generalise this literature by letting the combination weights follow more general schemes. Sieve estimation is used to optimise the score of the generalised density combination where the combination weights depend on the variable one is trying to forecast. Specific attention is paid to the use of piecewise linear weight functions that let the weights vary by region of the density. We analyse these schemes theoretically, in Monte Carlo experiments and in an empirical study. Our results show that the generalised combinations outperform their linear counterparts.JEL Codes: C53

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Section: Scoring Rulesmentioning

confidence: 99%

Section: Extensions: Interpreting the Weightsmentioning

confidence: 99%

Section: Extensions: Interpreting the Weightsmentioning

confidence: 99%

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Generalised density forecast combinations

Kapetanios

Mitchell

Price

et al. 2015

Journal of Econometrics

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“…Thus, further research is advisable to adjust the standard VaR predictions of the n-GARCH models based on csl scoring rule rather than the observed frequency Diks et al (2011).…”

Section: Discussionmentioning

confidence: 99%

“…While Hartz et al (2006), model the long VaR only, we try to extend their analysis by correcting the VaR for both long and short positions based on the aforementioned GARCH models (n-GARCH and n-EGARCH). Additionally, we evaluate models based on the censored likelihood (csl) scoring rule proposed by Diks, Panchenko, and Van Dijk (2011) in addition to the well-known Christoffersen's LR test. Empirical validation shows that considering asymmetry in conditional variance generally leads to improvements in accurately forecasting oneday-ahead VaR based on the bias-correction method for long and short positions, which is somewhat confirmed by the csl scoring rule.…”

Section: Introductionmentioning

confidence: 99%

Improving Value-at-Risk Estimation from the Normal EGARCH Model

Mahsa

Sajjad

2017

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Returns in financial assets display consistent excess kurtosis and skewness, implying the presence of large fluctuations not forecasted by Gaussian models. This paper applies a resampling method based on the bootstrap and a bias-correction step to improve Value-at-Risk (VaR) forecasting ability of the n-EGARCH (normal EGARCH) model and correct the VaR for both long and short positions. Our aim is to utilize the advantages of this model, but still use the bootstrap resampling method to accurate for the tendency of the model tomiscalculate the VaR. Empirical results indicate that the bias-correction method can improve the n-GARCH and n-EGARCH VaR forecasts so much that the acquired VaR predictions are different from the proposed probability. Additionally, allowing asymmetry in the conditional variance using the EGARCH model with normal distribution instead of GARCH improves the performance of the bias-correction method in forecasting the VaR for almost all considered indices. Moreover, the bias-corrected n-EGARCH model performs better than the simple t-EGARCH model. Thus, it seems that this model can take account of both the asymmetry in the conditional variance and leptokurtosis in returns distribution. However, we find that the superiority of the bias-corrected n-EGARCH model over the t-EGARCH model is not completely confirmed for short positions based on the censored likelihood scoring rule. IntroductionSince the Basle Committee (1995; began allowing banks to implement internal VaR models for calculating capital requirements, various methods have been proposed to achieve this purpose. However, the theoretical and computational complexity of these methods has also been raised.

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Forecast verification for extreme value distributions with an application to probabilistic peak wind prediction

Friederichs

Thorarinsdottir

2012

Environmetrics

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Predictions of the uncertainty associated with extreme events are a vital component of any prediction system for such events. Consequently, the prediction system ought to be probabilistic in nature, with the predictions taking the form of probability distributions. This paper concerns probabilistic prediction systems where the data are assumed to follow either a generalized extreme value (GEV) distribution or a generalized Pareto distribution. In this setting, the properties of proper scoring rules that facilitate the assessment of the prediction uncertainty are investigated, and closed form expressions for the continuous ranked probability score (CRPS) are provided. In an application to peak wind prediction, the predictive performance of a GEV model under maximum likelihood estimation, optimum score estimation with the CRPS, and a Bayesian framework are compared. The Bayesian inference yields the highest overall prediction skill and is shown to be a valuable tool for covariate selection, while the predictions obtained under optimum CRPS estimation are the sharpest and give the best performance for high thresholds and quantiles. Copyright © 2012 John Wiley & Sons, Ltd.

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Likelihood-based scoring rules for comparing density forecasts in tails

Cited by 138 publications

References 58 publications

Generalised density forecast combinations

Generalised density forecast combinations

Improving Value-at-Risk Estimation from the Normal EGARCH Model

Forecast verification for extreme value distributions with an application to probabilistic peak wind prediction

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