All these are described in an appendix to the paper The Continuous Wavelet Transform: A Primer. Choices about normalizations, conversion from scales to frequencies, formula used for the Continuous Wavelet Transform, and related transforms, determination of the Cone of Influence, smoothing, etc. When implementing the transforms, some choices had, naturally, to be made. For example, AWT.m and AWTV2.m correspond to the old and new versions, respectively.
To name the new files, we added V2 to the name of the old files. For replication of our previous papers, we kept the old functions in our toolbox. We also added a new significance test for the wavelet power spectrum, using the exact theoretical distribution when the null is a AR(0) or AR(1). June 17, 2014: We changed the way the phase-difference is computed.For a mathematical explanation, see section 4 of the paper "The Continuous Wavelet Transform: A Primer", updated version, which is included in the toolbox. The concepts of partial and multiple wavelet coherency are coded now. Finally one can move beyond bivariate analysis. This toolbox is now able to perform multivariate wavelet analysis. January 10, 2011: There was a mistake with the bootstrap procedures associated with the significance test, which was corrected on this day.(2007), who kindly provided us with their code.Īpart from some computational choices and the correction of some typos, there are four main differences: the capacity of using an entire family of analyzing wavelets, the Generalized Morse Wavelets (as well as the famous Morlet Wavelet), the possibility of changing the wavelet parameters, allowing for greater flexibility, different null hypothesis for testing significance, which are more common in economics and other social sciences, and (after 2018) the possibility of estimating the wavelet gain and the partial wavelet gain. Compo () and also on some modified versions of functions written by Bernard Cazelles et al. Some of our functions are based on (parts of) functions written by Christopher Torrence and Gilbert P. The new version contains the scripts necessary to replicate our papers "Estimating the Taylor rule in the time-frequency domain" (joint work with Manuel Martins) and "California's Carbon Market and Energy Prices: A Wavelet Analysis" (joint work with Rita Sousa). Examples - The old version contains matlab scripts and the data necessary to generate the pictures associated with each of the Examples in Section 7 of the paper The Continuous Wavelet Transform: A Primer.WaveletTransforms - containing functions to compute the (Analytic) Wavelet Transform, Wavelet Gain and Partial Wavelet Gain, Cross-Wavelet Transform, Wavelet Coherency, Wavelet Phase Difference, etc
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