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I plot a time-series for observation as you can see in the plot:

enter image description here

I tried to detrend the time series by 3 different approaches which are: 1) differences, 2) detrended fluctuation analysis, and 3) discrete wavelet transform, thus I obtain the attached plot:

enter image description here

In order to apply discrete wavelet transform approach I followed the directions provided in Help page of Mathematica to make detrending i.e I used the below code:

dwdfa = DiscreteWaveletTransform[data, SymletWavelet[3], 2, 
  Padding -> "Extrapolated"]

and then I calibrated the SymletWavelet and refinement parameters to make the detrended series correlated with the other approaches I mean SymletWavelet[3],and 2, .

My question here is would please explain me how to figure out those parameters correctly without making such calibration. I read some theoretical explanations but still I am fresh in wavelet analysis and most of time I get confused about this.

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  • $\begingroup$ Can you make your data available ? Also, does the de-trending have to be done through Wavelet Analysis or any other approach would be acceptable? $\endgroup$ – Anton Antonov May 17 '16 at 13:59
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    $\begingroup$ Look at question (69953) for a couple of solutions $\endgroup$ – Sektor May 17 '16 at 14:15
  • $\begingroup$ @AntonAntonov, I am trying to get more about different approaches of detrending, hence I am trying to understand wavelet more. $\endgroup$ – Mehmet May 19 '16 at 8:42
  • $\begingroup$ @Sektor, Thank you for your comment however, still I did not understand what is the best coefficient that I can figure out without using the other methods. In other words, Iam interested in understanding the nature of fluctuation in my time series in by extracting only the fluctuation component. The provided question gives more smooth data than extracting the fluctuation component $\endgroup$ – Mehmet May 19 '16 at 9:12
  • $\begingroup$ GraphicsGrid[ Map[ListLinePlot[#, PlotTheme -> "Detailed"] &, Map[Last, Map[dwd[{___, #}] &, {0, 1}], {2}], {2}]] where dwd is the DiscreteWaveletTransform of your data. This will give you an insight into your data set. Also -- search the documentation for DiscreteWaveletTransform and read under Details and Options. View sample plot $\endgroup$ – Sektor May 19 '16 at 10:35

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