This paper proposes generalization of the popular realized volatility framework by allowing its measurement in the time-frequency domain and bringing robustness to both noise as well as jumps. Based on the generalization of Fan and Wang (2007) approach using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we present new, general theory for wavelet decomposition of integrated variance. Using wavelets, we not only gain decomposition of the realized variance into several investment horizons , but we are also able to estimate the jumpsconsistently . Basing our estimator in the two-scale realized variance framework of Zhang et al. (2005) , we are able to utilize all available data and get unbiased estimator in the presence of  noise as well. The theory is also tested in a large numerical study of the small sample performance of the estimators and compared to other popular realized variation estimators under different simulation settings with changing noise as well as jump level  . The results reveal that our wavelet-based estimator is able to estimate and forecast the realized measures with the greatest precision. Another notable contribution lies in the application of the presented theory. Our time-frequency estimators not only produce more efficient estimates, but also decompose the realized variation into arbitrarily chosen investment horizons. The results thus provide a better understanding of the dynamics of stock markets .
We introduce wavelet-based methodology for estimation of realized variance allowing its measurement in the time-frequency domain . Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the realized variance into several investment horizons and jumps . Basing our estimator in the two-scale realized variance framework , we are able to utilize all available data and get feasible estimator in the presence of microstructure noise as well. The estimator is tested in a large numerical study of the finite sample performance and is compared to other popular realized variation estimators . We use different simulation settings with changing noise as well as jump level in different price processes including long memory fractional stochastic volatility model . The results reveal that our wavelet-based estimator is able to estimate and forecast the realized measures with the greatest precision. Our time-frequency estimators not only produce feasible estimates, but also decompose the realized variation into arbitrarily chosen investment horizons. We apply it to study the volatility of forex futures during the recent crisis at several investment horizons and obtain the results which provide us with better understanding of the volatility dynamics .
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present new, general theory for wavelet decomposition of integrated variance. Using wavelets, we not only gain decomposition of
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We apply it to study the volatility of forex futures during the recent crisis at several investment horizons and obtain the results which provide us with
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dynamics of stock markets
volatility dynamics