With regards to your questions, first draft of some detailed answers:
[Sanity Check for Wavelets](http://files.lossofgenerality.com/sanityWLT.pdf)
i. The last plots in the pdf are the denoised data which was not included in the original stuff I sent you.
ii. if you need the images from this file, all are available in jpg could zip and send you
1. I like to hammer the code and keep looking for bugs, the more we question the code the better, happier I am :)
2. I love writing live code tutorials to make sure I learn myself and could explain the concepts, so there is always ancillary coding for that matter. There are geniuses out there who just know things, I am not one of them, so when I talk about code it is about learning and aiding in thinking about the research, not about a final thing with definite veracity i.e. lots of bugs ;)
3. Wavelets like anything else have artifacts and they need to be learned and experimented with e.g. aliasing and padding.
4. Change of definitions: People keep talking about periodicity of El Nino for example, I understand Local Periodicity in order to be able to deal with discrete finite historical data. Inferences must be made cognizant of the fact that frequency or periodicity or amplitude are localized in time (or the varying parameter of the t-series function). At such time t, forecast-able periodicity is x , if you remove the localization then I do not understand the arguments and inferences
I go back to your blog and try to work on your questions and concerns.