The Wick theorem for non-Gaussian distributions and its application for noise filtering of correlated q-Exponentialy distributed random variables

TL;DR

This paper extends Wick's theorem to non-Gaussian q-Exponential distributions and applies it to develop an algorithm for estimating correlation matrices from spectral moments of correlated, non-Gaussian time series.

Contribution

It introduces a Wick theorem for q-Exponential distributions and uses it to create a novel algorithm for correlation matrix estimation in non-Gaussian data.

Findings

Derived Wick theorem for q-Exponential distribution

Developed an algorithm for correlation matrix estimation

Applied the method to spectral moments of time series

Abstract

We derive the Wick theorem for the q-Exponential distribution. We use the theorem to derive an algorithm for finding parameters of the correlation matrix of q-Exponentialy distributed random variables given empirical spectral moments of the time series.