Comparing Volatility Forecasts with Density-Based Evaluation
Summary
The document reviews research comparing foreign-exchange volatility forecasts from variations of GARCH models. The studies construct realized volatility from squared intraday returns, including adjustments intended to reduce market microstructure bias, and assess forecasts with regression, encompassing, and superior predictive ability methods. The question reports that raw intraday GARCH forecasts performed better while daily GARCH forecasts performed worse in the cited comparison.
The accepted response highlights a limitation of point forecast evaluation: loss functions comparing realized volatility with a single forecast value do not assess the full predictive distribution. It suggests comparing density forecasts, which can represent uncertainty and distributional shape and may therefore provide information relevant to risk management. A cited empirical article is offered as an illustration. The discussion is a brief suggestion rather than a full review; it supplies no competing findings or detailed evaluation of the proposed density methods.
Key ideas
- The reviewed studies compare multiple GARCH variants for forecasting FX volatility.
- Realized volatility is constructed from intraday squared returns, with adjustments for microstructure bias.
- The document reports better results for raw intraday GARCH and worse results for daily GARCH in the cited study.
- Point forecast losses do not evaluate the full predictive distribution.
- Density forecast comparisons can capture distributional information relevant to risk management.
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Full text
# Question regarding volatility forecasting using High Frequency Data
# Question regarding volatility forecasting using High Frequency Data
Hi guys this is my first question on the Quantitative Finance section of the Stack Exchange network. I am currently reviewing the paper by Professor Alan E. Speight and David G. McMillan 'Daily FX Volatility Forecasts: Can the GARCH(1,1) Model be Beaten using High Frequency Data?'. These are main characteristics of the pape:
- The authors try to further investigate the question of the paper by Hansen and Lunde 'A forecast comparison of volatility models: does anything beat a GARCH(1,1)?'.
- They use multiple variations of the GARCH class as forecasting models.
- They construct the realised volatility as the sum of squared returns and they also account for microsturure bias by using bias adjusted measures of realized volatility.
- As forecasting appraisal techniwues they use the Mincer Zarnowith regression and its GLS adjusted version by Patton and Sheppard(2009), the encompassing technique by Chong and Henry(1986) and the SPA test of Hansen (2005). Their results suggests that the raw intraday GARCH gives better forecasts whereas the daily GARCH gives the worse forecasts. My question is, are there any aspects, or advances in the field that MCMillan and Speight didn't incorporate? Any conflicting results? Any weaknesses? All suggestions are welcomed.
## Answer by Malick (score 2, accepted)
https://quant.stackexchange.com/a/27619
A limitation of both papers is they focus on point estimates, i.e they compare $\sigma_{t}$ with $h_{t}$ in the loss functions of the SPA Tests. A possible suggestion to overcome it, is to use a loss function based on density forecast, in order to capture the whole forecast density distribution and not only a single point. This may have important implications for risk management.
You can find an illustration of density forecast comparison in the following empirical article:
Wilhelmsson, A. (2013). Density Forecasting with Time-Varying Higher Moments : Journal of Forecasting, The ssrn version is here.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.