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This article studies the joint value-at-risk (VaR) and expected shortfall (ES) regression for a wide class of location-scale time series models including autoregressive and moving average models with generalized autoregressive conditional heteroscedasticity errors. In contrast to the quasi-maximum likelihood estimation, we estimate the model parameters with the aim of more accurate VaR and ES estimation. Then, we show consistency and asymptotic normality for parameter estimators under weak regularity conditions. Finally, a simulation study and a real data analysis are shown to illustrate our results.

This paper employs a novel approach to model the conditional distribution of China’s GDP growth with time-varying location, scale, and shape parameters. By decomposing the parameters into permanent and transitory components and introducing a series of macroeconomic variables, this study examines the factors that influence the time-varying risks of China’s GDP growth. The findings suggest a significant difference between permanent and transitory changes in the Chinese economy and show that macroeconomic variables impact all three moments. Despite being occasionally susceptible to adverse downside risks, China’s economy exhibits strong resilience and rapid recovery.

It is of great significance to study the risk spillover effect between soybean futures markets in China and the United States under extreme circumstances.A dynamic model based on the average method and the method of the bureau of digit conditional value at risk are combined to study.The risk spillover effects of Chinese soybean futures market influenced by policy and economic environment change is studied.And it analyses the risk spillover effects influenced by spot market,downstream products of soybean,macro-economic variables,international market trading,etc.It is found that different policies and economic environments affected the soybean futures market risk spillover effects in different ways,such as reserve policy stability of China's soybean futures price fluctuations,the night trading system to increase the interaction of the agricultural product futures market of China and the United States to increase the degree of impact on the domestic market in the international market.At the same time,the study shows that each control variable has a different contribution to the change in the risk spillover effect of the Chinese and American agricultural futures markets in different periods.For example,soybean oil futures price and WTI crude oil price have a great influence on the risk spillover effect in the early stage of the night trading system.The impact of shipping indices,exchange rates and WTI crude oil prices was at a low level during the COVID-19 pandemic.

Expected shortfall (ES), which conveys information regarding potential exceedances beyond the value-at-risk (VaR), is an important measure to characterize the properties of the tails of distribution. In this article, we study two two-step estimation procedures for ES regression with censored responses. Considering the potential dependence between the censoring variable and the covariates, two locally weighted estimation algorithms are proposed based on local Kaplan–Meier estimation and the joint elicitability of VaR and ES. The potential applications of this work are manifold, especially survival analysis, pharmacodynamic analysis, and sociological investigations. The resulting estimators are shown to be consistent. Extensive simulations demonstrate that the proposed method performs quite well in finite samples, with regard to estimation bias and mean squared errors. Last, the analysis of a real dataset illustrates the usefulness of our developed methodologies.

In order to investigate the dynamic dependency structure  between the S&P 500 stock index and 11 different U.S. sector indexes, and measure systemic risk. We first propose a new dynamic copula model with Markov regime-switching and macroeconomic component, and use a simulation study to verify its advantages. Macroeconomic components identified by principal component analysis and independent component analysis are added into the evolution of the copula parameter as exogenous variables to study the influence of macroeconomic factors on the interdependence between variables. Then, the estimation method of systemic risk measure conditional value-at-risk (CoVaR) in the proposed dynamic copula model is given. Finally, we provide an empirical analysis based on the above data and models. We find that when extreme events occur in the S&P500, the CoVaRs corresponding to sector indexes are distinctly time-varying, and the occurrence of major events have a greater impact on the CoVaR of each index. The consideration of Markov regime-switching parameters and macroeconomic factors improves the ability to estimate dependent structures. In addition, different macroeconomic factors have different influences on the interdependence between sector indexes and the overall S&P. U.S. unemployment rate is the most important macroeconomic factor for most sectors.

在动态Copula函数中加入外生变量,构建了TV-Copula-X模型,在定义"波动率惊喜"的基础上,从均值溢出和波动溢出两个角度研究了金砖国家股市间相依结构是否会受到美国股市的影响.选取金砖四国和美国股市的数据进行实证研究,实证结果显示,金砖国家之间在收益率和波动率上均有显著的相依关系.金砖国家波动率之间全部呈现非对称的相依结构,然而仅部分国家收益率之间存在非对称的相依结构.美国股市对部分金砖国家间相依关系产生一定的影响,并且当金融危机发生或者当金砖国家间发生正向积极事件时,金砖国家股市间的相关性都会增强.