We developed an implementation of a novel shift variance theorem of the fast wavelet transform (FWT), suitable to the multiresolution analysis of streaming univariate datasets, using compactly supported Daubechies Wavelets. The theorem is used to reduce the computational complexity of the FWT, and also to reduce drastically the number of wavelet coefficients to be estimated in forecasting the one step ahead discrete wavelet transform. For this reason, any FWT performed using the found shift variance properties is herein named reduced FWT. An effective real value prediction of a sampled input time series can be obtained performing the inverse DWT of an estimated crystal, and this is the purpose of the proposed predictor herein named Wa.R.P. (Wavelet transform Reduced Predictor). The C++ code implementing the FWT and the novel theorem is available to research purposes, and to build efficient industrial applications.
Stocchi, M., & Marchesi, M. (2018). Fast wavelet transform assisted predictors of streaming time series. SoftwareX, 8, 1–4. https://doi.org/10.1016/j.softx.2017.09.006