The paper by Andrew J. Patton explores the impact of using imperfect volatility proxies on the evaluation and comparison of conditional variance forecasts. It highlights that standard methods, such as the Diebold-Mariano (DM) and West (1996) tests, can lead to incorrect inferences when the volatility proxy is noisy. The author derives necessary and sufficient conditions for a loss function to ensure that the ranking of competing forecasts remains robust to noise in the volatility proxy. These conditions are related to those for quasi-maximum likelihood estimation and result in a class of "robust" loss functions that differ in their treatment of over-prediction and under-prediction. The paper also provides an empirical illustration using IBM return volatility forecasts, demonstrating the effectiveness of the proposed robust loss functions in comparing forecasts. The findings suggest that less noisy volatility proxies, such as intra-day range and realized variance, reduce distortion but still may lead to significant differences in forecast rankings. The paper concludes by discussing the broader implications for other latent variable forecasting problems and the potential for extending the results to handle different types of proxies and support sets.The paper by Andrew J. Patton explores the impact of using imperfect volatility proxies on the evaluation and comparison of conditional variance forecasts. It highlights that standard methods, such as the Diebold-Mariano (DM) and West (1996) tests, can lead to incorrect inferences when the volatility proxy is noisy. The author derives necessary and sufficient conditions for a loss function to ensure that the ranking of competing forecasts remains robust to noise in the volatility proxy. These conditions are related to those for quasi-maximum likelihood estimation and result in a class of "robust" loss functions that differ in their treatment of over-prediction and under-prediction. The paper also provides an empirical illustration using IBM return volatility forecasts, demonstrating the effectiveness of the proposed robust loss functions in comparing forecasts. The findings suggest that less noisy volatility proxies, such as intra-day range and realized variance, reduce distortion but still may lead to significant differences in forecast rankings. The paper concludes by discussing the broader implications for other latent variable forecasting problems and the potential for extending the results to handle different types of proxies and support sets.