Backtesting VaR and Expectiles with Realized Scores

24 Pages Posted: 5 Aug 2017

See all articles by Fabio Bellini

Fabio Bellini

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Ilia Negri

Universita di Bergamo

Mariya Pyatkova

UniversitĂ  degli Studi di Milano-Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Date Written: May 12, 2017

Abstract

Several statistical functionals such as quantiles and expectiles arise naturally as the minimizers of the expected value of a scoring function, a property that is called elicitability (see Gneiting, 2011 and the references therein). The existence of such scoring functions gives a natural way to compare the accuracy of different forecasting models, and to test comparative hypotheses by means of the Diebold-Mariano test (see e.g. Ziegel and Nolde, 2016). In this paper we suggest a procedure to test the accuracy of a quantile or expectile forecasting model in an absolute sense, as in the original Basel I backtesting procedure of Value-at-Risk. To this aim, we study the asymptotic and finite-sample distributions of empirical scores for Normal and Uniform i.i.d. samples. We compare on simulated data the empirical power of our procedure with alternative procedures based on empirical identification functions (i.e. in the case of VaR the number of violations) and we find an higher power in detecting at least misspecification in the mean. We conclude with a real data example where both backtesting procedures are applied to AR(1)-Garch(1,1) models fitted to SP500 logreturns for VaR and expectiles’ forecasts.

Keywords: Backtesting, Forecasting, Value at risk, Expectiles

Suggested Citation

Bellini, Fabio and Negri, Ilia and Pyatkova, Mariya, Backtesting VaR and Expectiles with Realized Scores (May 12, 2017). Available at SSRN: https://ssrn.com/abstract=3012932 or http://dx.doi.org/10.2139/ssrn.3012932

Fabio Bellini (Contact Author)

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Milano, Milan
Italy

Ilia Negri

Universita di Bergamo ( email )

Via Salvecchio, 19
Bergamo, 24129
Italy

Mariya Pyatkova

UniversitĂ  degli Studi di Milano-Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Milano, 20126
Italy

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