Realized Wavelet Jump-GARCH model: Can wavelet decomposition of volatility improve its forecasting? ✩ Jozef Barunik a,b, , Lukas Vacha a,b a Institute of Economic Studies, Charles University, Opletalova 21, 110 00, Prague, CR b Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod Vodarenskou Vezi 4, 182 00, Prague, Czech Republic Abstract 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. Keywords: wavelet decomposition, jumps, volatility forecasting, Realized GARCH JEL: C14, C53, G17 1. Introduction Much of the recent popularity of realized volatility is mainly due to its two distinct implications for practical estimation and forecasting. The first relates to the measurement of realizations of the ✩ We are grateful to David Veredas and Karel Najzar for many useful comments and suggestions. We are also grateful to seminar participants at the Modeling High Frequency Data in Finance 3 in New York (July 2011) and Computational and Financial Econometrics in London (December 2011) for many useful discussions. The support from the Czech Science Foundation under the 402/09/H045 project is gratefully acknowledged. Email address: barunik@utia.cas.cz (Jozef Barunik ) Preprint submitted to Elsevier May 20, 2022 arXiv:1204.1452v1 [q-fin.ST] 6 Apr 2012