Fast wavelet transform assisted predictors of streaming time series

We explore the shift variance of the decimated, convolutional Discrete Wavelet Transform, also known as Fast Wavelet Transform. We prove a novel theorem improving the FWT algorithm and implement a new prediction method suitable to the multiresolution analysis of streaming univariate datasets using compactly supported Daubechies Wavelets. An effective real value forecast is obtained synthesizing the one step ahead crystal and performing its inverse DWT, using an integrated group of estimating machines. We call Wa.R.P. (Wavelet transform Reduced Predictor) the new prediction method. A case study, testing a cryptocurrency exchange price series, shows that the proposed system can outperform the benchmark methods in terms of forecasting accuracy achieved. This result is confirmed by further tests performed on other time series. Developed in C++, Standard 2014 conformant, the code implementing the FWT and the novel Shift Variance Theorem is available to research purposes and to build efficient industrial applications.