# wavelet decomposition for time series signal

Is it possible to use stationary wavelet decomposition as a tool to extract wavelet features for a time series? I can see how it works for image cases, but for a time series prediction problem say $x_i$, $i = 1,2,3,\cdots,n$ and you want to predict $x_{n+1}$, is it possible to use stationary wavelet decomposition to extract features and if yes why it makes sense?

A signal is just a 1D image. So if you can make it work for images, why not for signals? Pun aside, discrete wavelets combine multiscale smoother and differential operators, so they are been used as trend and singularity detectors for a while. Wavelet coefficients can be turned into feature vectors, directly or by condensating them across subband. For instance, wavelet subband coefficients are often believed to follow generalized Laplace-Gauss model distributions: $$A_{\alpha,\beta}\exp{\left(-\frac{|x-m|}{\beta}\right)^\alpha}\,.$$
And you can form a vector of subband features with estimated $$\alpha_j$$ and $$\beta_j$$ at each scale $$j$$ for classification. Using stationary wavelets adds some shift invariance (see Difference between “equivariant to translation” and “invariant to translation”). Then, wavelet coefficients can be used as time-frequency anchors as in the Shazam music matching technique (An Industrial-Strength Audio Search Algorithm), or the deep-learning mimicking technique from the scattering wavelet transform developed by S. Mallat and coauthors.