Abstract
Comparative evaluation of forecasts of statistical functionals relies on comparing averaged losses of competing forecasts after the realization of the quantity Y, on which the functional is based, has been observed. Motivated by high-frequency finance, in this paper we investigate how proxies for Y—say volatility proxies—which are observed together with Y can be utilized to improve forecast comparisons. We extend previous results on robustness of loss functions for the mean to general moments and ratios of moments, and show in terms of the variance of differences of losses that using proxies will increase the power in comparative forecast tests. These results apply both to testing conditional as well as unconditional dominance. Finally, we numerically illustrate the theoretical results, both for simulated high-frequency data as well as for high-frequency log returns of several cryptocurrencies.
Acknowledgments
We would like to thank Andrew Patton and Tilmann Gneiting for pointers to the literature, and in particular for bringing the paper by Hoga and Dimitriadis (2022) to our attention. Then we would like to thank Timo Dimitriadis for providing various general and detailed, helpful comments on the paper. The authors are grateful for the suggestions and comments of two anonymous reviewers, which helped to improve the paper.
Citation
Hajo Holzmann. Bernhard Klar. "Using proxies to improve forecast evaluation." Ann. Appl. Stat. 17 (3) 2236 - 2255, September 2023. https://doi.org/10.1214/22-AOAS1716
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