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...

Dzhaparidze and Spreij (Stoch Process Appl, 54:165–174, <CitationRef CitationID="CR5">1994</CitationRef>) showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This class contains...</citationref>

This article focuses on a recent concept of covariation for processes taking values in a separable Banach space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$B$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>B</mi> </math> </EquationSource> </InlineEquation> and a corresponding quadratic variation. The latter is more general than the classical one of Métivier and Pellaumail. Those notions are associated with some subspace <InlineEquation ID="IEq2"> <EquationSource...</equationsource></inlineequation></equationsource></equationsource></inlineequation>