In this paper, we introduce new forecast encompassing tests for the risk measure Expected Shortfall (ES). Forecasting and forecast evaluation techniques for the ES are rapidly gaining attention through the recently introduced Basel III Accords, which stipulate the use of the ES as primary market risk measure for the international banking regulations. Encompassing tests generally rely on the existence of strictly consistent loss functions for the functionals under consideration, which do not exist for the ES . However, our encompassing tests are based on recently introduced loss functions and an associated regression framework which considers the ES jointly with the corresponding Value at Risk (VaR). This setup facilitates several testing specifications which allow for both, joint tests for the ES and VaR and stand-alone tests for the ES. We present asymptotic theory for our encompassing tests and verify their finite sample properties through various simulation setups. In an empirical application, we utilize the encompassing tests in order to demonstrate the superiority of forecast combination methods for the ES for the IBM stock .
We introduce new forecast encompassing tests for the risk measure Expected Shortfall (ES). The ES currently receives much attention through its introduction into the Basel III Accords, which stipulate its use as the primary market risk measure for the international banking regulation. We utilize joint loss functions for the pair ES and Value at Risk to set up three ES encompassing test variants. The tests are built on misspecification robust asymptotic theory and we verify the finite sample properties of the tests in an extensive simulation study. We use the encompassing tests to illustrate the potential of forecast combination methods for different financial assets .
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In this paper, we
We
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Forecasting and forecast evaluation techniques for the ES are rapidly gaining attention through the recently introduced
The ES currently receives much attention through its introduction into the
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the use of the ES as
its use as the
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regulations. Encompassing tests generally rely on the existence of strictly consistent
regulation. We utilize joint
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functionals under consideration, which do not exist for the ES . However, our encompassing tests are based on recently introduced loss functions and an associated regression framework which considers the ES jointly with the corresponding
pair ES and
R
(VaR). This setup facilitates several testing specifications which allow for both, joint tests for the ES and VaR and stand-alone tests for the ES. We present asymptotic theory for our encompassing tests and verify their
to set up three ES encompassing test variants. The tests are built on misspecification robust asymptotic theory and we verify the
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through various simulation setups. In an empirical application, we utilize
of the tests in an extensive simulation study. We use
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in order to demonstrate the superiority
to illustrate the potential
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the ES for the IBM stock
different financial assets