A Bayesian encompassing test using combined value-at-risk estimates
针对条件自回归风险价值（CAViaR）模型众多难以选择最优的问题，提出一种贝叶斯包含检验，评估各模型预测与组合模型的关系，为使用组合条件VaR估计预测分位数风险提供依据。
The Value at Risk (VaR) is a risk measure that is widely used by financial institutions in allocating risk. VaR forecast estimation involves the conditional evaluation of quantiles based on the currently available information. Recent advances in VaR evaluation incorporate conditional variance into the quantile estimation, yielding the Conditional Autoregressive VaR (CAViaR) models. However, the large number of alternative CAViaR models raises the issue of identifying the optimal quantile predictor. To resolve this uncertainty, we propose a Bayesian encompassing test that evaluates various CAViaR models predictions against a combined CAViaR model based on the encompassing principle. This test provides a basis for forecasting combined conditional VaR estimates when there are evidences against the encompassing principle. We illustrate this test using simulated and financial daily return data series. The results demonstrate that there are evidences for using combined conditional VaR estimates when forecasting quantile risk.