论文标题
根据对边界的推断，对处于风险的价值和预期短缺的多步骤预测进行了涵盖测试
Encompassing Tests for Value at Risk and Expected Shortfall Multi-Step Forecasts based on Inference on the Boundary
论文作者
论文摘要
我们提出了基于灵活链接（或组合）功能的风险（VAR）的预期不足（ES）的预测测试。我们的设置允许测试包含凸预报组合的测试和链接功能，这些链接功能排除了组合的VAR和ES预测。由于基于这些链接函数的测试涉及在零假设下的参数空间边界上的参数，因此我们在边界上的非标准渐近理论基于非标准渐近理论。我们的仿真研究表明，基于我们的新链路功能的包含测试优于基于一步和多步骤预测的无限制线性链路函数的测试。我们进一步说明了建议的测试的潜力，这些测试在针对标准普尔500指数的预测VAR和ES的真实数据分析中。
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.
