Decomposing the dynamics in time series data with spectral analysis

Many educational and social phenomena are dynamic and change over time. To study such phenomena, intensive longitudinal data and time-series analyses are essential. Yet such methods remain largely underused in educational sciences, due to their perceived complexity and the dominance of group-level prediction. Complex Dynamic Systems (CDS) perspectives offer promising tools for studying educational phenomena that unfold over time, addressing limitations of traditional nomothetic approaches. CDS emphasises idiographic methods that capture individual, context-dependent processes and within-person change. This paper introduces an accessible approach to CDS research by explaining and illustrating how time-series decomposition with spectral analysis can reveal trends, cycles, and level of synchronisation. By breaking down time-series into interpretable components, researchers can better understand dynamic educational processes and avoid misrepresenting complex phenomena. The current paper illustrates the application of time-series decomposition and spectral analysis with time series data of teacher behaviour, student behaviour, and teacher physiology in four classrooms. The application of time-series analysis is discussed considering the differences in the teachers’ dynamic profiles as well as the potential to study a large variety of other educational topics.