# Detrending a time-series by means of Discrete Wavelet Transform

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

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:

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,

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, .
• Look at question (69953) for a couple of solutions – Sektor May 17 '16 at 14:15
• 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 – Sektor May 19 '16 at 10:35