Given a sequence of fractional frequency deviates, we investigate the relationship between the sample variance of these deviates and the total variance (Totvar) estimator of the Allan variance. We demonstrate that we can recover exactly twice the sample variance by renormalizing the Totvar estimator and then summing it over dyadic averaging times 1, 2, 4, . . . , 2 along with one additional ter...

Abstract In this paper we introduce a new criterion in order to measure the variance and covariance risks in financial markets. In an asset allocation framework with stochastic (co)variances, we consider the possibility to invest also in variance swaps, that are assets which span the volatility as well as the co-volatility risks. We provide explicit solutions for the portfolio optimization prob...

Wavelets have recently been a subject of great interest in geophysics, mathematics and signal processing. The discrete wavelet transform can be used to decompose a time series with respect to a set of basis functions, each one of which is associated with a particular scale. The properties of a time series at different scales can then be summarized by the wavelet variance, which decomposes the v...