The Runs Test and Reverse Arrangements Test Do Not Accurately Assess Signal Stationarity

Abstract

PURPOSE Fourier analysis of electromyographic or heart rate variability data, for example, assumes that the signals being analyzed are stationary in the time and frequency domain. The runs test and the reverse arrangements tests have been recommended for use in determining whether a signal is stationary. The purpose of this study was to assess the ability of these tests to correctly characterize the stationarity of synthesized signals. METHODS Stationary signals were created using LabVIEW software. The signals were designed to have a sampling rate of 1000 Hz and duration of 25 seconds. All signals were either pure sine waves at a fixed frequency, sine waves with random noise, or the sum of two sine waves at fixed frequencies. The synthesized signals were analyzed using both the runs test and reverse arrangements test as described by Bendat and Piersol. Non-stationarity was defined as a resulting Z score greater than 1.96. RESULTS All of the synthesized stationary signals yielded Z scores for both the runs test (Z scores ranged from 123 to 158) and reverse arrangements test (Z scores ranged from 173 to 193) that were highly significant, i.e., the tests had a specificity of zero. CONCLUSIONS The results of this analysis indicate that the runs test and reverse arrangements test are not appropriate for assessing signal stationarity for all signals and should not be used as such. The failure of these tests under these conditions is not surprising given that they were designed to determine if a signal is random. Signals such as EMG and heart rate variability can be stationary but are not random.