Cycles in Politics: Wavelet Analysis of Political Time Series


  • We thank Joshua Goldstein for the data used in Goldstein (1988). Previous versions of this article were presented at the 2009 APSA Toronto meeting and at the Lisbon Group on Institutions and Public Policy 2009/2010 paper series. We thank Paul Beck, Cees van der Eijk, Nathan Kelly, Sandro Mendonça, and Luís Catela Nunes, as well as the other participants in these meetings for their valuable comments and suggestions. Criticisms and suggestions from three anonymous referees and the editor Rick K. Wilson are also gratefully acknowledged. The usual disclaimer applies. The data and MatLab scripts necessary to replicate all our results are available for download at In the same website, the reader can find and freely download a wavelet MatLab toolbox that we wrote. We are currently working on producing a similar toolbox programmed in R, which will be available in the same website. See the online appendix for more details on our toolbox.

Luís Aguiar-Conraria is Assistant Professor, Department of Economics and NIPE, University of Minho, Campus de Gualtar, 4710-057 Braga-Portugal ( Pedro C. Magalhães is Researcher, Institute of Social Sciences, University of Lisbon, Av. Prof. Aníbal de Bettencourt 9, 1600-189 Lisboa-Portugal ( Maria Joana Soares is Associate Professor, Department of Mathematics and Applications, NIPE, University of Minho, Campus de Gualtar, 4710-057 Braga-Portugal (


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 around 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 article, we present the tools of wavelet analysis and apply them to the study of two lingering puzzles in the political science literature: the existence of cycles in election returns in the United States and in the severity of major power wars.