This paper aims to investigate the efficiency of the value-at-risk (VaR) backtests in the model selection from different types of generalised autoregressive conditional heteroskedasticity (GARCH) models with skewed and non-skewed innovation distributions. Extensive simulation is carried out to compare the model selection based on VaR backtests and Akaike Information Criteria (AIC). When the model is given but the innovation distribution is one of the six selected distributions which may be skewed or non-skewed, the simulation results show that both AIC and the VaR backtests succeed in selecting the correct innovation distribution from the set of six distributions under consideration. This indicates that both AIC and the VaR backtests are able to distinguish between skewed and non-skewed distributions when the innovation distribution is misspecified. Using an empirical data from NASDAQ index, we observe that the selected combination of model and innovation distribution based on the smallest AIC does not agree with that selected by using the in-sample VaR backtests. Examination of confidence limits for VaR and the expected shortfall forecasts under various loss functions provides evidence that the selected combination of model and innovation distribution using the VaR backtests tends to possess smaller mean absolute percentage error and logarithmic loss.

中文翻译：

---

基于风险价值回测方法的GARCH类型模型的模型选择

本文旨在研究具有偏斜和非偏斜创新分布的不同类型的广义自回归条件异方差（GARCH）模型在模型选择中的风险价值（VaR）回测的效率。进行了广泛的仿真，以比较基于VaR回测和Akaike信息标准（AIC）的模型选择。当给出模型但创新分布是六个可能偏斜或非偏斜分布之一时，仿真结果表明，AIC和VaR回测都成功地从以下六个分布中选择了正确的创新分布考虑。这表明当创新分布未正确指定时，AIC和VaR回测都能区分偏斜分布和非偏斜分布。使用来自纳斯达克指数的经验数据，我们观察到基于最小AIC选择的模型和创新分布的组合与使用样本内VaR回测选择的结果不一致。对VaR的置信限和各种损失函数下的预期短缺预测的检验提供了证据，表明使用VaR回测选择的模型和创新分布的组合往往具有较小的平均绝对百分比误差和对数损失。我们观察到，基于最小AIC选择的模型和创新分布的组合与使用样本内VaR回测选择的组合不一致。对VaR的置信限和各种损失函数下的预期短缺预测的检验提供了证据，表明使用VaR回测选择的模型和创新分布的组合往往具有较小的平均绝对百分比误差和对数损失。我们观察到，基于最小AIC选择的模型和创新分布的组合与使用样本内VaR回测选择的组合不一致。对VaR的置信限和各种损失函数下的预期短缺预测的检验提供了证据，表明使用VaR回测选择的模型和创新分布的组合往往具有较小的平均绝对百分比误差和对数损失。