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https://doi.org/10.1016/j.apr.2018.07.001

has been cited by the following article:

• TITLE: Air Quality Risk Measurement Based on CAViaR Model: A Case Study of PM10 in Beijing

  AUTHORS: Peng Sun, Fuming Lin

  KEYWORDS: PM10, VaR, kth Power Expectile, CAViaR Model

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.10, October 20, 2023

  ABSTRACT: Air pollution control has always been a global challenge, and significant progress has been made in recent years in controlling air pollutants. However, in some major cities, air pollutant concentrations still exceed the standards. Some scholars have used linear models or conditional autoregressive iterative models to apply the VaR method to predict pollutant concentrations. However, traditional methods based on quantile regression estimation can lead to inadequate risk estimates. Therefore, we propose a method based on the Conditional Autoregressive Value at Risk (CAViaR) model, which uses the kth power expectile regression to estimate VaR. This method does not specify the type of the distribution of data, is easier to calculate the asymptotic variance, more sensitive to extreme values. Applying our method to the data of PM10 in Beijing, we investigate the fitting effects in the case of k = 1, k = 2, and k = 1.9 through predictive tests. The results show that the kth power expectile regression estimates are better than quantile and expectile regression estimates to some extent.