A Nonstationarity Test for the Spectral Analysis of Physiological Time Series with an Application to Respiratory Sinus Arrhythmia

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Abstract
The spectral analysis of time series requires the signal to be at least weakly statonary; i.e., the mean, (co‐) variance, and spectrum of the time series should not vary from segment to segment. It is commonly assumed that psychophysiological time series are not stationary. This study introduces a nonstationarity test to the psychophysiological literature, which is derived from evolutionary spectral analysis. Basically, the test consists of a double window technique in both the time and frequency domains, leading to a two‐way analysis of variance for times and frequencies. In the current study, the nonstationarity test is applied to heart rate data obtained in a typical psychophysiological setting. Heart rate and respiration were measured in four age groups under four conditions—rest, paced breathing, vigilance, and reaction time. The results indicate that only few physiological time series were completely stationary. However, for every subject, and in every condition stationary strectches could be found that were long enough to apply spectral analysis. Spectral measures (power, coherence, and phase spectra) were then compared for stationary parts of the data and the total data. This comparison indicated that nonstationarity affects all spectral measures. Most importantly, Stationarity × Task Condition × Frequency Band interactions were observed for coherence and phase spectra, and there were significant interactions with age for each of the spectral indices. These findings suggest that nonstationarity may result in biased outcomes of significance tests of the effects of task manipulations on the spectral indices of cardiac time series. Thus, it was concluded that the stationarity test should be routinely applied in the spectral analysis of physiological time series. In addition, it was suggested that the nonstationarity test has an even wider range of application that might be of interest to the psychophysiologist.