  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.
