Conditional Autoregressive Value-at-Risk and Conditional Autoregressive Expectile have become two popular approaches for direct measurement of market risk. Since their introduction several improvements both in the Bayesian and in the classical framework have been proposed to better account for asymmetry and local non-linearity. Here we propose a unified Bayesian Conditional Autoregressive Risk Measures approach by using the Skew Exponential Power distribution. Further, we extend the proposed models using a semiparametric P-Spline approximation answering for a flexible way to consider the presence of non-linearity. To make the statistical inference we adapt the MCMC algorithm proposed in Bernardi et al. (2018) to our case. The effectiveness of the whole approach is demonstrated using real data on daily return of five stock market indices.

有条件的自回归风险价值和有条件的自回归期望值已成为直接测量市场风险的两种流行方法。自从引入以来，已经提出了贝叶斯和经典框架中的一些改进，以更好地说明非对称性和局部非线性。在这里，我们提出了一种利用偏斜指数幂分布的统一贝叶斯条件自回归风险度量方法。此外，我们使用半参数P样条逼近来扩展提出的模型，以考虑非线性的灵活方式。为了进行统计推断，我们采用了Bernardi等人提出的MCMC算法。（2018）。使用有关五个股票市场指数每日收益的真实数据证明了整个方法的有效性。