 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.
<clarity>  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.
 Based on the generalization of Fan and Wang (2007) approach using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the 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.