Realized Wavelet Jump-GARCH model: Can wavelet decomposition of volatility improve IT’S forecasting?

Jozef Barunik


Department of Macroeconomics and Econometrics

Institute of Economic Studies, Faculty of Social Sciences,

Charles University in Prague

Opletalova 21, 110 00, Prague 1

Czech Republic


Department of Econometrics

Institute of Information Theory and Automation

Academy of Sciences of the Czech Republic

Pod Vodarenskou Vezi 4, 18000, Prague 8

Czech Republic


Tel: +420776259273

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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.


This talk represents work with L.Vacha