I am wondering if anyone else in the RATS forum has any interest in developing a wavelet transform, and using this to set up some forecasting algorithms. I have proposed this to the main office, but am curious to know if there is wider interest.
The prequel to this is that wavelets are a new class of transforms, which incorporate both time domain and frequency domain properties. For most econometric models, regression-based models work well. In the sciences, neural nets have often been preferred. The frequency domain forecasting routine has actually proven to be extremely useful in forecasting certain data sets from the physical sciences. The reason is that many scientific data sets contain cycles at regular frequencies.
Cycles at irregular periodicities (i.e., the periodicity can vary from one cycle to the next) create a wholly different kind of forecasting problem. In fact, the obvious example is the business cycle. Here, models incorporating regular frequencies are not particularly useful. However, wavelet-based forecasting methods may be quite promising.
Of the various wavelets that are available in the literature, the best is probably the Daubechies wavelet. So what I am proposing is two routines, to do a wavelet transform (WT, analogous to the Fast Fourier Transform) and an inverse wavelet transform (IWT, analogous to IFT). In the interest of expediency, this would be limited to the transforms. Programs like MATLAB and R apparently have wavelet transform routines.
One interesting property of wavelet transforms is that (in contrast to the spectral forecasting routine, which is entirely univariate) it would in principle be possible to set up multivariate models.
Is there widespread interest in this? Also, let me ask the main office to report on how much it would cost to develop this capability. Thank you.