In this paper, we propose a forecasting model for volatility based on its decomposition to several investment horizons and jumps. As a forecasting tool, we utilize Realized GARCH framework of Hansen et al. (2011), which models jointly returns and realized measures of volatility. For the decomposition, we use jump wavelet two scale realized volatility estimator (JWTSRV) of Barunik and Vacha (2012). While the main advantage of our time-frequency estimator is that it provides us with realized volatility measure robust to noise as well as with consistent estimate of jumps, it also allows to decompose volatility into the several investment horizons  . On currency futures data covering the period of recent financial crisis , we compare forecasts from Realized GARCH (1,1) model using several  measures. Namely, we use the realized volatility, bipower variation, two- scale realized volatility, realized kernel and our jump wavelet two scale realized volatility. We find that in-sample as well as out-of-sample performance of the model significantly differs based on the realized measure used. When JWTSRV estimator is used, model produces significantly best forecasts . We also utilize jumps and build Realized Jump-GARCH model. Utilizing the decomposition obtained by our estimator, we finally build Realized Wavelet-Jump GARCH model, which uses estimated jumps as well as volatility at several investment horizons . Our Realized Wavelet-Jump GARCH model proves to further improve the volatility forecasts. We conclude that realized volatility measurement in the time-frequency domain and inclusion of jumps improves the volatility forecasting considerably.
In this paper, we propose a forecasting model for volatility based on its decomposition to several investment horizons and jumps. As a forecasting tool, we use Realized GARCH framework which models jointly returns and realized measures of volatility. Using jump wavelet two scale realized volatility estimator (JWTSRV) , we first decompose the returns volatility into several investment horizons and jumps and then utilise this decomposition in a newly proposed Realized Jump-GARCH and Realized Wavelet-Jump GARCH models . On currency futures data covering the period of recent financial crisis we moreover compare the forecasts from Realized GARCH model using several additional realized volatility measures. Namely, we use the realized volatility, bipower variation, two-scale realized volatility, realized kernel and jump wavelet two scale realized volatility. We find that in-sample as well as out-of-sample performance of the model significantly differs based on the realized measure used. When JWTSRV estimator is used, model produces significantly best forecasts . Our Realized Wavelet-Jump GARCH model proves to further improve the volatility forecasts. We conclude that realized volatility measurement in the time-frequency domain and inclusion of jumps improves the volatility forecasting considerably.
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of Barunik and Vacha (2012). While the main advantage of our time-frequency estimator is that it provides us with realized volatility measure robust to noise as well as with consistent estimate of jumps, it also allows to decompose volatility into the
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. We also utilize jumps and build Realized Jump-GARCH model. Utilizing the decomposition obtained by our estimator, we finally build Realized Wavelet-Jump GARCH model, which uses estimated jumps as well as volatility at several investment horizons