This paper proposes an enhanced approach to modeling and forecasting
volatility using high frequency data. Using a forecasting model based on
Realized GARCH with multiple time-frequency decomposed realized volatility
measures, we study the influence of different timescales on volatility
forecasts. The decomposition of volatility into several timescales approximates
the behaviour of traders at corresponding investment horizons. The proposed
methodology is moreover able to account for impact of jumps due to a recently
proposed jump wavelet two scale realized volatility estimator. We propose a
realized Jump-GARCH models estimated in two versions using maximum likelihood
as well as observation-driven estimation framework of generalized
autoregressive score. We compare forecasts using several popular realized
volatility measures on foreign exchange rate futures data covering the recent
financial crisis. Our results indicate that disentangling jump variation from
the integrated variation is important for forecasting performance. An
interesting insight into the volatility process is also provided by its
multiscale decomposition. We find that most of the information for future
volatility comes from high frequency part of the spectra representing very
short investment horizons. Our newly proposed models outperform statistically
the popular as well conventional models in both one-day and multi-period-ahead
forecasting
