Cycles in Politics: Wavelet Analysis of Political Time Series

Abstract

Po ol li it ti ic cs s: : W Wa av ve el le et t A An na al ly ys si is s o of f P Po ol li it ti ic ca al l T Ti im me e--S Se er ri ie es s" " L Lu uí ís s A Ag gu ui ia ar r--C Co on nr ra ar ri ia a P Pe ed dr ro o C C. . M Ma ag ga al lh hã ãe es s M Ma ar ri ia a J Jo oa an na a S So oa ar re es s NIPE WP 25/ 2011 " "C Cy yc cl le es s i in n P Po ol li it ti ic cs s: : W Wa av ve el le et t A An na al ly ys si is s o of f P Po ol li it ti ic ca al l T Ti im me e--S Se er ri ie es s" " L Lu uí ís s A Ag gu ui ia ar r--C Co on nr ra ar ri ia a P Pe ed dr ro o C C. . M Ma ag ga al lh hã ãe es s M Ma ar ri ia a J Jo oa an na a S So oa ar re es s Abstract Spectral analysis and ARMA models have been the most common weapons of choice for the detection of cycles in political time-series. Controversies about cycles, however, tend to revolve about an issue that both techniques are badly equipped to address: the possibility of irregular cycles without fixed periodicity throughout the entire time-series. This has led to two main consequences. On the one hand, proponents of cyclical theories have often dismissed established statistical techniques. On the other hand, proponents of established techniques have dismissed the possibility of cycles without fixed periodicity. Wavelets allow the detection of transient and coexisting cycles and structural breaks in periodicity. In this paper, we present the tools of wavelet analysis and apply them to the study to two lingering puzzles in the political science literature: the existence to cycles in election returns in the United States and in the severity of major power wars. 1 3 The paper proceeds as follows. The next section uses empirical and constructed numerical examples to illustrate the use of ARMA models and spectral analysis in the detection of cyclesand their shared inability to deal with irregular and transient cycles. We will show that this inability does not extend to wavelet analysis. Following that section, we present the three basic tools in wavelet analysis: the wavelet power spectrum, cross-wavelets, and phase-differences.Equiped with these tools, we will develop two applications to real world political time-series data. The first is the analysis of presidential and congressional election returns in the UnitedStates from 1854 to 2008. The second application of wavelet analysis concerns the severity of major power wars from 1495 to 1975, using well-established data in the literature (Levy 1983;Goldstein 1988). In the last section, we sketch a research agenda in political science where the use of wavelet analysis may shed light on important empirical and theoretical discussions. In the appendix, we describe how to computationaly implement the wavelet tools.

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