wavemulcor: Wavelet Routines for Global and Local Multiple Correlation

Wavelet routines that calculate single sets of wavelet multiple correlations (WMC) and cross-correlations (WMCC) out of n variables. They can later be plotted in single graphs, as an alternative to trying to make sense out of several sets of wavelet correlations or wavelet cross-correlations. The code is based on the calculation, at each wavelet scale, of the square root of the coefficient of determination in a linear combination of variables for which such coefficient of determination is a maximum. The code provided here is based on the wave.correlation routine in Brandon Whitcher's waveslim R package Version: 1.6.4, which in turn is based on wavelet methodology developed in Percival and Walden (2000) <doi:10.1017/CBO9780511841040>; Gençay, Selçuk and Whitcher (2002) <doi:10.1016/B978-012279670-8.50013-6> and others. Version 2 incorporates wavelet local multiple correlations (WLMC). These are like the previous global WMC but consisting in one single set of multiscale correlations along time. That is, at each time t, they are calculated by letting a window of weighted wavelet coefficients around t move along time. Six weight functions are provided. Namely, the uniform window, Cleveland's tricube window, Epanechnikov's parabolic window, Bartlett's triangular window and Wendland's truncated power window and the Gaussian window. Version 2.2 incorporates an auxiliary function that calculates local multiple correlations (LMC). They are calculated by letting move along time a window of weighted time series values around t. Any of the six weight functions mentioned above can be used.

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