Evaluating volatility and interval forecasts

A widely used approach to evaluating volatility forecasts uses a regression framework which measures the bias and variance of the forecast. We show that the associated test for bias is inappropriate before introducing a more suitable procedure which is based on the test for bias in a conditional mean forecast. Although volatility has been the most common measure of the variability in a financial time series, in many situations confidence interval forecasts are required. We consider the evaluation of interval forecasts and present a regression-based procedure which uses quantile regression to assess quantile estimator bias and variance. We use exchange rate data to illustrate the proposal by evaluating seven quantile estimators, one of which is a new non-parametric autoregressive conditional heteroscedasticity quantile estimator. The empirical analysis shows that the new evaluation procedure provides useful insight into the quality of quantile estimators.