Wavelet Packets of Fractional Brownian Motion: Asymptotic Analysis and Spectrum Estimation

Wavelet estimation for operator fractional Brownian motion ∗†‡

Operator fractional Brownian motion (OFBM) is the natural vector-valued extension of the univariate fractional Brownian motion. Instead of a scalar parameter, the law of an OFBM scales according to a Hurst matrix that affects every component of the process. In this paper, we develop the wavelet analysis of OFBM, as well as a new estimator for the Hurst matrix of bivariate OFBM. For OFBM, the un...

Definition, properties and wavelet analysis of multiscale fractional Brownian motion

Wavelet analysis of the multivariate fractional Brownian motion

The work developed in the paper concerns the multivariate fractional Brownian motion (mfBm) viewed through the lens of the wavelet transform. After recalling some basic properties on the mfBm, we calculate the correlation structure of its wavelet transform. We particularly study the asymptotic behavior of the correlation, showing that if the analyzing wavelet has a sufficient number of null fir...

Wavelet Analysis of Fractional Brownian Motion in Multifractal Time

We study fractional Brownian motions in multifractal time, a model for multifractal processes proposed recently in the context of economics. Our interest focuses on the statistical properties of the wavelet decomposition of these processes, such as residual correlations (LRD) and stationarity, which are instrumental towards computing the statistics of wavelet-based estimators of the multifracta...

Wavelet entropy and fractional Brownian motion time series

We study the functional link between the Hurst parameter and the normalized total wavelet entropy when analyzing fractional Brownian motion (fBm) time series—these series are synthetically generated. Both quantifiers are mainly used to identify fractional Brownian motion processes [L. Zunino, D.G. Pérez, M. Garavaglia, O.A. Rosso, Characterization of laser propagation through turbulent media by...