Dears,
I need to apply a specific technique based on wavelet transform in an experimental time series but this depends on a "quasi-normal" distribution of the data.
In the paper where this technique is described, the authors wrote:
"Check the histograms of the time series to ensure that they are not too far from normally distributed. Consider transforming the time series, if the pdf’s of the time series are far from Gaussian. When choosing a transformation, it is preferable to choose an analytic transformation such as taking the logarithm if the data are lognormally distributed. In other cases, the simple “percentile” transformation we used for the BMI might be useful..." (Grinsted, A., Moore, J. C., and Jevrejeva, S.: Application of the cross wavelet transform and wavelet coherence to geophysical time series, Nonlin. Processes Geophys., 11, 561–566, https://doi.org/10.5194/npg-11-561-2004, 2004).
So, following this instruction I applied the QQPlot to my data and, initially, I noted that the data do not are similar to a normal distribution. In the sequence, I analyzed the "transformed" time series using a log transformation (I did this because my experimental data have only positive values) and, the results of the QQPlot showed me that the transformed time series (too) do not have a behavior near the normal distribution. You can see the results of QQPlots in the sequence:
QQPlots of Original Data (lrft panel) and Log of Original Data (right panel)
I would like to know what others transform I can try to use in my original data by the "transformed" time series to have the same possibility to be closed to a quasi-normal distribution as I need to apply the analysis technique.
I appreciate that to receive suggestions and references about these possible transformations.
Regards! :)