WaveletComp: A guided tour through the R-package

WaveletComp is an R package for 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 — which objects should be added to a plot (for example, the ridge of wavelet power, contour lines indicating significant periodicity, arrows indicating the leading/lagging series), which kind and degree of smoothing is desired in wavelet coherence plots, which color palette to use, how to define the layout of the time axis (using POSIXt conventions), and others. Technically, we have developed vectorand matrix-based implementations of algorithms to reduce computation time. Easy and intuitive handling was given high priority. Even though we provide some details concerning the mathematical foundation of the methodology implemented in WaveletComp, the present guide is not intended to give an introduction to wavelet analysis. The goal here is to give a series of constructed as well as real-world examples to illustrate the use and functionality of WaveletComp, with statistical arguments in mind.