I have been working on modelling a time series using wavelets for a long time. I am quite familiar with the wavelet theory and all...However, I have a big understanding issue and really appreciate it if you help. Basically I am using wavelets for feature extraction: I have decomposed the time series into J resolution levels. Then extracted "some" of the coefficients ( before time t) in each level. Finally found a nonlinear mapping between those coefficients and the value of time series at time t. I got really good results. My question is, how am I taking advantage of the properties of wavelet in this way? Can anybody share their experience?
Thank you for taking the time to read this.
I think you need to be more specific about how is that non-linear mapping you found, because as far as I understand the wavelet transform it is a linear mapping onto the set of basis function.
If you are extracting features then your application falls in the field of pattern recognition and wavelet is useful because it is a generalization of the Fourier Transform, giving you good resolution in frequency and good resolution in time, telling you where those frequencies occurred in your data. If you want to see from another perspective it could be seen as a "bandpass" filter where you only see only the time-frequencies of your interest.
Beyond that if you could provide a more detailed information I could try to bring a little more help.