Before revision:  This study establishes autoregressive models to determine the maximum and minimum volatilities, where the ratio of minimum volatility to maximum volatility can measure volatility uncertainty. By utilizing the value at risk (VaR) predictor model under volatility uncertainty, we introduce the risk and uncertainty, and show that the autoregressive model of volatility uncertainty is a powerful tool in predicting the VaR for a benchmark dataset  .
After revision:  This study establishes autoregressive models to determine the parameters of G-normal distribution, i.e., the return, maximal and minimal volatilities of the time series. Utilizing the value at risk (VaR) predictor model under volatility uncertainty, we introduce the risk and uncertainty, and show that the autoregressive model of volatility uncertainty is a powerful tool in predicting the VaR for a benchmark dataset .