Question regarding volatility forecasting using High Frequency Data

Question

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 1

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.