A1590
Title: Networks inference with (quasi-)analytic wavelets
Authors: Sophie Achard - CNRS LJK (France) [presenting]
Irene Gannaz - INP-Grenoble (France)
Abstract: In the general setting of long-memory multivariate time series, the long-memory characteristics are defined by two components. The long-memory parameters describe the autocorrelation of each time series. The long-run covariance measures the coupling between time series and general phase parameters. It is of interest to estimate the long-memory, long-run covariance and general phase parameters of time series generated by this wide class of models, although they are not necessarily Gaussian nor stationary. This estimation is thus not directly possible using real wavelets decomposition or Fourier analysis. The purpose is to define an inference approach based on a representation using quasi-analytic wavelets. It is first shown that the covariance of the wavelet coefficients provides an adequate estimator of the covariance structure, including the phase term. Consistent estimators based on a local Whittle approximation are then proposed. Simulations highlight a satisfactory behavior of the estimation of finite samples on multivariate fractional Brownian motions. An application on a real neuroscience dataset is presented, where long-memory and brain connectivity are inferred.
