On Waves in War and Elections Wavelet Analysis of Political Time-Series

Spectral analysis and ARMA models have been the most established weapons of choice for the detection of cycles in time series data. However, such techniques are only appropriate when periodic components are time invariant. This has led some scholars to disregard the possibility of irregular cycles. We aim to contribute to further reconsideration of the possibility of cycles in political phenomena by introducing wavelet analysis. Its main contribution comes from the ability to estimate the spectral characteristics of a time series as a function of time, thus revealing how its different periodic components change over time, while preserving rigorous standards of statistical inference. We demonstrate the usefulness of wavelet analysis with two applications. The first concerns the possibility of long-cycles in wars, one of the central puzzles in the international relations sub-field. The second concerns election returns in presidential and congressional elections in the United States, where the existence of cyclical patterns has been equally controversial. Contrary to the prevailing wisdom, wavelet analysis allows the detection of transient and coexisting cycles, shedding some light over phenomena that have remained unaddressed so far.