I would suggest you start by investigating your data using the Time-Frequency toolbox for matlab (http://tftb.nongnu.org/), using the tutorial (http://tftb.nongnu.org/tutorial.pdf) as a guide. This will give you a practical introduction to time-frequency analysis, with many examples. The references in the tutorial can be used to guide you further.

As far as R is concerned, I can suggest you this package https://cran.r-project.org/web/packages/wmtsa/wmtsa.pdf. If, on the other hand, you need some theoretical hint, you can consult Percival/Walden "Wavelet methods for time series analysis". Finally, there is a third reference, the Nason's book "Wavelet Methods in Statistics with R". It is a sort of middlepoint between a pure theoretical and just practical approach. You can find in both the latter references some info concerning the choice of multiresolution level (which has to fit properly your model!)

For better result in wavelet transform, the best decomposition level and best wavelet base are both have equal importance. If you show your result I can try to give explanation of that.

The answer depends on the feature type you are trying to find. But since you are talking about periodicity, I recommend that you start by doing FFT and find what are your significant frequencies. Then decompose your signal with a wavelet that has direct link between scale and frequency such as Morlet, Mexican hat, or Shanon (Harmonic). Then based on the specific relation between scale and frequency chose the scales that you want to decompose your signal into. Then do the decomposition. Then look along the lines of constant scales, and notice how the wavelet transform changes along these lines with respect to time. This tells lots of information about how regular the periodicity is, is there frequency change,  and where in time they occur! 

Best of luck

In order to find trend and periodicity of time series you don't need necessarily to use wavelet transformation. since you mentioned that you are using Matlab, here are some simply commands for trends and periodicity of time series:

trend: output = getTrend(data)

or for 3D: output = trend(data,dim) which returns the trend along dimension

have a look at https://it.mathworks.com/matlabcentral/fileexchange/46363-trend

periodicity: pxx = periodogram(data,window,nfft)

I hope it helps,

Naomi

I found EEGLAB software package (free) very handy when running wavelet analysis on Matlab with limited programming experience in this environment. It gets you up and running and is reasonably stable.

First of all, in wavelet analysis, it is necessary choose the mother wavelet. The choice of mother wavelet is based on the similarity of mother wavelet to the shape of analyzed signal and on its suitability for detecting signal changes. In Matlab, for level of decomposition, you can find the maximum level possible considering a specific mother wavelet (wname) in this way:

L = wmaxlev(S,wname)

The maximum level is the last level for which at least one coefficient is correct.

Hi Martin,

I am interested in using EEGLAB software package, could you give me some insight into the processing. I am analyzing Rainfall data.

Check this.

https://elcvia.cvc.uab.es/article/view/v18-n1-sunkara

https://rpubs.com/ibn_abdullah/rwcoher for your ref. or https://www.youtube.com/watch?v=2xIX9Lu-uLw&t=76s . Follow this video step by step!

You may be interested in this ABC radio blog on East Coast Australia Tsunami probability (https://www.abc.net.au/radionational/programs/scienceshow/how-tsunami-have-impacted-australia%E2%80%99s-east-coast-and-a-new-appr/13758616 ) cheers col