Testing Stationarity with Wavelet-Based Surrogates

Traditional methods of using surrogate data to test for linearity of time-series data can be extended into the time-frequency domain to test for stationarity. Surrogates are time series that are created directly from the original dataset through manipulation and seek to replicate important properties of the original dataset. By comparing the original signal to the surrogates, additional structure in the original dataset not explained by the replicated properties may be revealed. The surrogates used for the purpose of testing stationarity are stationarized versions of an original signal that have the same Fourier amplitudes, but have randomized phases. Wavelet analysis is used in this method to transform the signals into the time-frequency domain and wavelet scalograms are used to quantitatively compare the original signal to the stationarized surrogate signals. Methods introduced in previous research compare the local and global spectral features of the surrogate signals with the local and global spectral features of the original signal to evaluate the stationarity of the signal as a whole. These methods are compared with a perceived new method, introduced here, that uses the surrogate-signal scalograms, which should contain no meaningful nonstationarity, to filter-out stationary portions of the original signal and noise, revealing where nonstationarity may be occurring within the signal. The methods are tested on a diverse set of generated signals as well as data from windstorms such as hurricanes and thunderstorms/downbursts, which may contain strong nonstationary features characterized by rapid changes in wind speed and direction. While several of the methods presented in previous research show good results with specific types of nonstationarity present, it is shown that the new technique of filtering out stationarity is better able to evaluate signals that contain many sources of nonstationarity. DOI: 10.1061/(ASCE)EM.1943-7889.0000484. (C) 2013 American Society of Civil Engineers.