Financial time series admits inherent uncertainty and randomness that changes over time. To clearly describe volatility uncertainty of the time series, we assume that the volatility of risky assets holds value between the minimum volatility and maximum volatility of the assets. 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  .
Based on law of large numbers and central limit theorem under nonlinear expectation, we introduce a new method of using G-normal distribution to measure financial risks. Applying max-mean estimators and small windows method, we establish 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 G-normal distribution, we show that the G-VaR model gives an excellent performance in predicting the VaR for a benchmark dataset comparing to many well-known VaR predictors .
R
Financial time series admits inherent uncertainty and randomness that changes over time. To clearly describe volatility uncertainty of the time series, we assume that the volatility of risky assets holds value between the minimum volatility and maximum volatility of the assets. This study establishes
Based on law of large numbers and central limit theorem under nonlinear expectation, we introduce a new method of using G-normal distribution to measure financial risks. Applying max-mean estimators and small windows method, we establish
R
maximum and minimum volatilities, where the ratio of minimum volatility to maximum volatility can measure volatility uncertainty. By utilizing
parameters of G-normal distribution, i.e., the return, maximal and minimal volatilities of the time series. Utilizing
R
volatility uncertainty, we introduce the risk and uncertainty, and
G-normal distribution, we
R
autoregressive model of volatility uncertainty is a powerful tool
G-VaR model gives an excellent performance
A
comparing to many well-known VaR predictors