Forecasting VaR based on Joint Quantile and ES Regression Models

Dimitriadis and Bayer (2019) proposed a new regression framework which simultaneously models the quantile and the Expected Shortfall (ES) of a response variable given a set of covariates. This framework allows the use of different covariate vectors to make combined predictions of the models. Combined forecasting methods often provide a more practical way to synthesize the information provided by individual forecasting methods. Expected loss ES as a risk measure that satisfies subadditivity, especially since the Basel Committee recommended it as an alternative risk measure in 2016, has received more attention. In this paper, under the regression framework of Dimitriadis and Bayer (2019), different quantile covariates are used to study the advantages and disadvantages of different risk prediction models for combined prediction. CAViaR-SAV-VaR quantile prediction method by introducing AR(1)-GARCH model and quantile regression. A series of combinations of each prediction model are performed to explore the optimal combination of prediction models. In this paper, a series of independent forecasting models and combinations of models are used to empirically analyze the daily logarithmic return data of my country's Shanghai Composite Index. The results show that the forecasting effect of the combined model based on CAViaR-SAV-VaR and RM is better than other model combinations.