Before revision: 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.
After revision: 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 maximum and minimum volatilities, where the ratio of minimum volatility to maximum volatility can measure volatility uncertainty.