Detecting and Estimating Multivariate Self-Similar Sources in High-Dimensional Noisy Mixtures

Nowadays, because of the massive and systematic deployment of sensors, systems are routinely monitored via a large collection of time series. However, the actual number of sources driving the temporal dynamics of these time series is often far smaller than the number of observed components. Independently, self-similarity has proven to be a relevant model for temporal dynamics in numerous applications. The present work aims to devise a procedure for identifying the number of multivariate self-similar mixed components and entangled in a large number of noisy observations. It relies on the analysis of the evolution across scales of the eigenstructure of multivariate wavelet representations of data, to which model order selection strategies are applied and compared. Monte Carlo simulations show that the proposed procedure permits identifying the number of multivariate self-similar mixed components and to accurately estimate the corresponding self-similarity exponents, even at low signal to noise ratio and for a very large number of actually observed mixed and noisy time series