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Encompassing Tests for Value at Risk and Expected Shortfall Multistep Forecasts Based on Inference on the Boundary

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  • Timo Dimitriadis
  • iaochun Liu
  • Julie Schnaitmann

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 that preclude crossings of the combined VaR and ES forecasts. As the tests based on these link functions involve parameters that 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 multistep 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.

Suggested Citation

  • Timo Dimitriadis & iaochun Liu & Julie Schnaitmann, 2023. "Encompassing Tests for Value at Risk and Expected Shortfall Multistep Forecasts Based on Inference on the Boundary," Journal of Financial Econometrics, Oxford University Press, vol. 21(2), pages 412-444.
    • Handle: RePEc:oup:jfinec:v:21:y:2023:i:2:p:412-444.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbab004
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    More about this item

    Keywords

    asymptotic theory on the boundary; joint elicitability; multistep ahead and aggregate forecasts; forecast evaluation and combinations;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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