Spectral and Cross-Spectral Analysis—A Tutorial for Psychologists and Social Scientists

Social scientists have become increasingly interested in using intensive longitudinal methods to study social phenomena that change over time. Many of these phenomena are expected to exhibit cycling fluctuations (e. g., sleep, mood, sexual desire). However, researchers typically employ analytical methods which are unable to model such patterns. We present spectral and cross-spectral analysis as means to address this limitation. Spectral analysis provides a means to interrogate time series from a different, frequency domain perspective, and to understand how the time series may be decomposed into their constituent periodic components. Cross-spectral extends this to dyadic data and allows for synchrony and time offsets to be identified. The techniques are commonly used in the physical and engineering sciences, and we discuss how to apply these popular analytical techniques to the social sciences while also demonstrating how to undertake estimations of significance and effect size. In this tutorial we begin by introducing spectral and cross-spectral analysis, before demonstrating its application to simulated univariate and bivariate individual and group-level data. We employ cross-power spectral density techniques to understand synchrony between the individual time series in a dyadic time series, and circular statistics and polar plots to understand phase offsets between constituent periodic components. Finally, we present a means to undertake nonparameteric bootstrapping in order to estimate the significance, and derive a proxy for effect size. A Jupyter Notebook (Python 3.6) is provided as supplementary material to aid researchers who intend to apply these techniques.