Volatility Forecast Evaluation and Comparison Using Imperfect Volatility Proxies

We show that the use of a conditionally unbiased, but imperfect, volatility proxy can lead to undesirable outcomes in some commonly used methods for evaluating and comparing conditional variance forecasts: the true conditional variance may be rejected as being sub-optimal, and an imperfect volatility forecast may be selected over the true conditional variance. We also consider the extent of the problem when more efficient volatility proxies, such as the intra-daily range or realised volatility, are used for forecast comparison. We derive necessary and sufficient conditions on the loss function for the ranking of competing volatility forecasts to be preserved when a volatility proxy is employed. Finally, we present a collection of tests of equal predictive ability that may be employed when only limited knowledge of the volatility forecast user’s loss function is available.