Stats › Volatility and VIX › GARCH against realised
High frequency data beats GARCH by a factor of two at one day, and loses to it at ten
| Model | Mark, 1 day | Yen, 1 day | Cross, 1 day | Mark, 10 day | Yen, 10 day | Cross, 10 day |
|---|---|---|---|---|---|---|
| Realised volatility VAR | 0.249 | 0.329 | 0.355 | 0.197 | 0.278 | 0.293 |
| GARCH | 0.096 | 0.297 | 0.300 | 0.082 | 0.263 | 0.328 |
| Exponential smoothing | 0.097 | 0.266 | 0.286 | 0.056 | 0.211 | 0.299 |
| VAR on absolute returns | 0.028 | 0.115 | 0.119 | 0.011 | 0.183 | 0.215 |
| Realised plus GARCH | 0.249 | 0.346 | 0.364 | not reported | not reported | not reported |
Out of sample r squared from forecast evaluation regressions. Interbank quotes for the mark and the yen against the dollar and the cross between them, 30 minute returns, 3,045 days from 1 December 1986 to 30 June 1999. In sample is 2,449 days to 1 December 1996 and out of sample is 596 days from 2 December 1996. A fractionally integrated model was estimated and omitted because its one and ten day predictions were close to GARCH.
For the mark against the dollar, a realised volatility model reaches an out of sample r squared of 0.249 at one day against 0.096 for GARCH. At ten days, for the yen against the mark, GARCH reaches 0.328 and the realised model 0.293.
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