Application of Wavelets to the Study of Political History
The use of wavelet analysis is already very common in a large variety of disciplines, such as physics, geophysics, astronomy, epidemiology, signal and image processing, medicine, biology, or oceanography. More recently, wavelet tools have also been applied successfully in the areas of economics and finance.
In spite of their increasing popularity in all these fields, wavelets are still very rarely used in other social sciences, namely, in political history or political science.
The purpose of this article is to present a self-contained introduction to the continuous wavelet transform, with special emphasis on its time-frequency localization properties and to illustrate the potential of this tool for problems in the area of political history, by considering a particular example – the discussion about the possible existence of cycles in the British electoral politics.
“The idea that social processes develop in a cyclical manner is somewhat like a ‘Lorelei.’...
KeywordsWavelet Analysis Window Function Continuous Wavelet Morlet Wavelet Wavelet Power Spectrum
- Chase-Dunn C, Willard A (1993) Systems of cities and world-systems: settlement size hierarchies and cycles of political centralization, 2000 BC – 1988 AD. IROWS working paper no. 5. http://irows.ucr.edu/papers/irows5/irows5.htm
- Enders W, Sandler T (2006) The political economy of terrorism. Cambridge University Press, Cambridge/New YorkGoogle Scholar
- Flandrin P (1988) Time-frequency and time-scale. In: IEEE fourth annual ASSP workshop on spectrum estimation and modeling, Minneapolis, pp 77–80Google Scholar
- Gabor D (1946) Theory of communications. J Inst Elec Eng 93:429–457Google Scholar
- Goldstein J (1988) Long cycles: prosperity and war in the modern age. Yale University Press, New HavenGoogle Scholar
- Goldstone JA (1991) Revolution and rebellion in the early modern world. University of California Press, Berkeley/Los AngelesGoogle Scholar
- Goupillaud P, Grossmann A, Morlet J (1984) Cycle-octave and related transforms in seismic signal analysis. Geophys J Roy Astron Soc 23:85–102Google Scholar
- Lachowicz P (2009) Wavelet analysis: a new significance test for signals dominated by intrinsic red-noise variability. IEE Trans Sign Proc. arXiv: 0906.4176v1Google Scholar
- Lilly JM, Olhede SC (2007) On the analytic wavelet transform. IEEE Trans Signal Process 1:1–15Google Scholar
- Stimson JA (1999) Public opinion in America: moods, cycles, and swings. Westview Press, BoulderGoogle Scholar
Books and Reviews
- Bachmann G, Beckenstein E, Narici L (1999) Fourier and wavelet analysis. Springer, New YorkGoogle Scholar
- Blatter C (1998) Wavelets: a primer. A K Peters/CRC Press, Naticks, MassachusettsGoogle Scholar
- Combes JM, Grossmann A, Tchamitchian P (eds) (1989) Wavelets: time-frequency methods and phase-space. In: Proceedings of international conference, Springer, Marseille, 14–18 DecGoogle Scholar
- Daubechies I (1993) Different perspectives on wavelets. In: Proceedings of symposium American mathematical, vol 47, ProvidenceGoogle Scholar
- Gallegati M, Semmler W (eds) (2014) Wavelet applications in economics and finance, vol 20, Dynamic modeling and econometrics in economics and finance. Springer, ChamGoogle Scholar
- Hubbard BB (1996) The world according to wavelets: the story of a mathematical technique in the making. A K Peters/CRC Press, Natick, MassachusettsGoogle Scholar
- Ruskai MB, Beylkin G, Coifman RR, Daubechies I, Mallat S, Meyer Y, Raphael LA (eds) (1991) Wavelets and their applications. Jones & Bartlett, BostonGoogle Scholar
- Strang G, Nguyen T (1996) Wavelets and filter banks. Wellesley-Cambridge, Wellesley, MassachusettsGoogle Scholar