Dear all,
I would like to ask you about filtering low frequencies with wavelet. To be more precise, I have a large data panels of financial time series and I would like to remove short-run oscillations (i.e. to remove high frequencies). What would be the advantages if I employed a Wavelet instead of a canonical low-pass filter? Should I get better results since Wavelet take into account the nonstationarity of time series? Or is there something else too?
Thank you all!
As you have mentioned that the wavelets take into account the non-stationarity of the data it would be better than the standard filtering. One problem that you can face in the wavelet filtering is the choice of the wavelets. You need to select the basis function that matches your data closely.
using the level of decomposition you can control the frequency bands that are classified as useful data or the noise. You can also perform band pass filtering by selecting the bands you want to keep. The scaling function is the low pass component and the wavelets are subsequent bands of higher and higher frequency.
One problem can be that wavelet basis as classically defined are not dependent on the data itself but like the fourier basis are fixed. This has been studied in the methods such as the empirical wavelet transform, Empirical Mode Decomposition, Diffusion Wavelets and Synchrosqueezing Wavelet transform etc
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