# Multivariate Hadamard self-similarity: testing fractal connectivity

@article{Wendt2017MultivariateHS, title={Multivariate Hadamard self-similarity: testing fractal connectivity}, author={Herwig Wendt and Gustavo Didier and S{\'e}bastien Combrexelle and Patrice Abry}, journal={arXiv: Statistics Theory}, year={2017} }

## 22 Citations

### Multivariate scale-free dynamics: Testing fractal connectivity

- Mathematics2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2017

A multivariate Gaussian stochastic process with Hadamard (i.e., entry-wise) self-similar scale-free dynamics, controlled by a matrix Hurst parameter H, that allows departures from fractal connectivity is introduced.

### Wavelet Domain Bootstrap for Testing the Equality of Bivariate Self-Similarity Exponents

- Mathematics2018 IEEE Statistical Signal Processing Workshop (SSP)
- 2018

This work construct and study a wavelet domain bootstrap test for the equality of self-similarity exponents from one single observation (time series) of multivariate data, and it is shown to be satisfactory for use on real world data.

### Tempered fractional Brownian motion: Wavelet estimation, modeling and testing

- MathematicsApplied and Computational Harmonic Analysis
- 2018

### On Multivariate Non-Gaussian Scale Invariance: Fractional Lévy Processes And Wavelet Estimation

- Mathematics2019 27th European Signal Processing Conference (EUSIPCO)
- 2019

This paper proposes a new process called operator fractional Lévy motion (ofLm) as a LÉvy-type model for non-Gaussian multivariate self-similarity, based on large size Monte Carlo simulations of bivariate ofLm with a combination of Gaussian and non- Gaussian marginals.

### Detection and Estimation of Delays in Bivariate Self-similarity: Bootstrapped Complex Wavelet Coherence

- MathematicsICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2019

The self-similarity paradigm enables the analysis of scale-free temporal dynamics and has been widely used in a large set of real-world applications. However, in a multivariate setting, delays…

### Bootstrap-based Bias Reduction for the Estimation of the Self-similarity Exponents of Multivariate Time Series

- MathematicsICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2019

An original wavelet domain bias reduction technique is developed assuming a single multivariate time series is available and this method leads to wavelet eigenanalysis-based estimation of multivariate Hurst exponents with significantly improved finite-sample performance than earlier state-of-the-art formulations.

### Asymptotics of bivariate local Whittle estimators with applications to fractal connectivity

- Mathematics
- 2020

### Demixing operator fractional Brownian motion

- Mathematics
- 2016

In this paper, we consider the problem of demixing a multivariate stochastic process made up of independent, fractional Brownian motion entries. The observable, mixed signal is then an operator…

### Multivariate scale-free temporal dynamics: From spectral (Fourier) to fractal (wavelet) analysis

- MathematicsComptes Rendus Physique
- 2019

### Two-step wavelet-based estimation for mixed Gaussian fractional processes

- Mathematics
- 2016

A mixed Gaussian fractional process {Y (t)}t∈R = {PX(t)}t∈R is a multivariate stochastic process obtained by pre-multiplying a vector of independent, Gaussian fractional process entries X by a…

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A multivariate Gaussian stochastic process with Hadamard (i.e., entry-wise) self-similar scale-free dynamics, controlled by a matrix Hurst parameter H, that allows departures from fractal connectivity is introduced.

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