Discrete Wavelet Transform can be used to extract the trend (by removing the fluctuations) of the time series. However, the selection of appropriate wavelet family and wavelet filter is a major issues. Are the selection of wavelet familiy and wavelet filter sensitive to the determining trend of time series? If it does then how it affect? Which wavelet families / filters are the mostly used for extracting trend of time series?
If I understood the question correctly, yes, the result of detrending perfored by wavelet filtering will slightly depend on the selected wavelet. However, the effect will be reduced if a wavelet decomposition level is high (the thresholded wavelet coefficients must correspond to the trend, this can be achived by an increased frequency resolution of the wavelet transform, i.e. higher decomposition level).
The impact of the wavelet decomposition-based detrending can be seen as small artifacts in the filtered signal.
Hello,
Sometimes, it is an important issue to choose appropriate wavelet family. In order to decompose a time series in to a filter-bank structure using wavelet, it can vary with wavelet family to be chosen. Sometime depending on different time series characteristics, you may got different results for different wavelet family. In that case, you can check the reconstruction error, or other statistics in order to choose appropriate family.
Actually, some researcher develop their own wavelet family for their own data analysis. Overall, using different wavelet family, you may get minor difference depending on the nature of data(i.e, too much fluctuation/outlier, etc.)
Basically, almost all wavelet families except Haar has 8 taps, but they are differ in terms of orthogonality, bi-orthogonality etc. properties. So, it is sometimes helpful to match the nature of data and wavelet family properties of getting more appropriate wavelet family.
Try to understand the nature of your data (test either orthogonality, bi-orthogonality, etc.), based on testing, select the relevant wavelet family.
Hello,
Here in the link, you will find details about wavelet and applications;
http://users.rowan.edu/~polikar/WAVELETS/WTpart1.html
Please follow the part 3 & Part 4. Thanks.
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