基于边界推断的风险价值和期望损失多步预测的综合检验
Encompassing Tests for Value at Risk and Expected Shortfall Multi-Step Forecasts based on Inference on the Boundary
摘要：
我们建议预测包含测试的预期短缺（ES）与风险价值（VaR）的基础上灵活的链接（或组合）功能。我们的设置允许测试包括凸预测组合和链接功能，排除交叉的组合风险值和ES预测。由于这些链接函数的基础上的测试涉及的参数是在零假设下的参数空间的边界上，我们推导出和基于我们的测试非标准渐近理论的边界上。我们的模拟研究表明，包含测试的基础上，我们的新的链接函数优于测试的基础上，无限制的线性链接函数的一步和多步预测。我们进一步说明了潜在的建议测试在一个真实的数据分析预测风险值和ES的标准普尔500指数。
英文摘要：
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.
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