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摘要翻译：
我们提出了一种基于灵活链接（或组合）函数的包含预期缺口(ES)和风险值(VaR)联合检验的预测方法。我们的设置允许测试包括凸预测组合和链接函数，这些函数排除了组合VaR和ES预测的交叉。由于基于这些链接函数的检验所涉及的参数在零假设下位于参数空间的边界上，因此我们推导出基于边界上的非标准渐近理论的检验。我们的仿真研究表明，对于一步和多步预测，基于新链路函数的包围测试优于基于无限制线性链路函数的测试。我们进一步说明了所提出的检验在实际数据分析中预测标准普尔500指数的VaR和ES的潜力。
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英文标题：
《Encompassing Tests for Value at Risk and Expected Shortfall Multi-Step
Forecasts based on Inference on the Boundary》
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作者：
Timo Dimitriadis and Xiaochun Liu and Julie Schnaitmann
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最新提交年份：
2020
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分类信息：
一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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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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PDF链接：
https://arxiv.org/pdf/2009.07341
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