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Encompassing tests for value at risk and expected shortfall multi-step forecasts based on inference on the boundary

Timo Dimitriadis, Xiaochun Liu and Julie Schnaitmann

No 11-2020, Hohenheim Discussion Papers in Business, Economics and Social Sciences from University of Hohenheim, Faculty of Business, Economics and Social Sciences

Abstract: We propose forecast encompassing tests for the Expected Shortfall (ES) jointly with the Value at Risk (VaR) based on flexible link (or combination) functions. Our setup allows testing encompassing for convex forecast combinations and for link functions which preclude crossings of the combined VaR and ES forecasts. As the tests based on these link functions involve parameters which are on the boundary of the parameter space under the null hypothesis, we derive and base our tests on nonstandard asymptotic theory on the boundary. Our simulation study shows that the encompassing tests based on our new link functions outperform tests based on unrestricted linear link functions for one-step and multi-step forecasts. We further illustrate the potential of the proposed tests in a real data analysis for forecasting VaR and ES of the S&P 500 index.

Keywords: asymptotic theory on the boundary; joint elicitability; multi-step ahead and aggregate forecasts; forecast evaluation and combinations (search for similar items in EconPapers)
JEL-codes: C12 C52 C58 (search for similar items in EconPapers)
Date: 2020
New Economics Papers: this item is included in nep-for, nep-ore and nep-rmg
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