Statistical significance test of intrinsic mode functions

Abstract

One of the preliminary tasks when analyzing a dataset is to determine whether it or its components contain useful information. The task is essentially a binary hypothesis testing problem in which a null hypothesis of pure noise is often pre-proposed. To test against the null hypothesis, the characteristics of noise need to be understood first, and often, these characteristics pertain to the analysis method used. In this paper, the characteristics of Gaussian white noise are studied by using the empirical mode decomposition (EMD) method. Statistical testing methods for Gaussian white noise for the intrinsic mode functions (IMFs) are designed based on the characteristics of Gaussian white noise by using EMD. These methods are applied to well-studied geophysical datasets to demonstrate the method’s validity and effectiveness.