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Wavelets: an implementation in R, and some applications
Wavelet methodology is a reasonable choice to study periodic phenomena in time series, particularly in the presence of potential frequency changes across time. Wavelets provide a workable compromise in the time and frequency resolution dilemma (resulting from the Heisenberg uncertainty principle) arising in this context. Applications in signal and image processing, medicine, geophysics and astronomy have been abounding since the early 1980s, but applications of wavelets in economic investigations are more recent. Growing interest in the application of wavelet methodology has brought forth several open-source packages for wavelet analysis in R. Our R package WaveletComp is a tool for the continuous wavelet-based analysis of univariate and bivariate time series. Wavelet functions are implemented in WaveletComp such that a wide range of intermediate and final results are easily accessible. The null hypothesis that there is no (joint) periodicity in the series is tested via p-values obtained from simulation, where the model to be simulated can be chosen from a wide variety of options. The reconstruction, and thus filtering, of a given series from its wavelet decomposition, subject to a range of possible constraints, is also possible. WaveletComp provides extended plotting functionality. Easy and intuitive handling is given high priority. Using R package WaveletComp, we present examples of wavelet transformations and their applications in financial econometrics and other areas. For example, we consider three equity markets, represented by stock indices DJIA (USA), FTSE 100 (UK), and EURO STOXX 50 (euro area), and find that the band of relevant frequencies has become narrower in return-to-volatility propagation values from year 2000 onwards; European stock markets have been more or less in phase since the introduction of the euro, while European and American stock markets have not.